M7180 Functional Analysis II

Faculty of Science
Autumn 2023
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Peter Šepitka, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 M3,01023
  • Timetable of Seminar Groups:
M7180/01: Mon 11:00–11:50 M3,01023, P. Šepitka
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005, 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1975, 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia, 1973, 408 s. URL info
Teaching methods
Lectures, seminars
Assessment methods
Two-hour written final exam (it is needed to reach at least 50 % of points) with oral evaluation of the exam with each student.
The conditions (especially regarding the form of the exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021.

M7180 Functional Analysis II

Faculty of Science
autumn 2021
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 12:00–13:50 M3,01023
  • Timetable of Seminar Groups:
M7180/01: Mon 11:00–11:50 M4,01024, P. Šepitka
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005, 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1975, 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia, 1973, 408 s. URL info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2019
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M7180/01: Mon 8:00–8:50 M3,01023, P. Šepitka
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005, 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1975, 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia, 1973, 408 s. URL info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
autumn 2017
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 9. to Fri 15. 12. Fri 12:00–13:50 M4,01024
  • Timetable of Seminar Groups:
M7180/01: Mon 18. 9. to Fri 15. 12. Fri 14:00–14:50 M4,01024, M. Veselý
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005, 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1975, 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia, 1973, 408 s. URL info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2015
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M7180/01: Mon 10:00–10:50 M6,01011, O. Došlý, M. Veselý
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in this subject area; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Spectrum of linear operators (repetition from the course Functional analysis I).
  • 2. Spectral theory of self-adjoint and symmetric operators.
  • 3. Symmetric and self-adjoint operators in Hilbert spaces: Deficiency indices, self-adjoint extension of a symmetric operator.
  • 4. Differential calculus in Banach spaces.
  • 5. Strictly and uniformly convex spaces.
  • 6. Integration of functions with values in Banach spaces.
  • 7. Degree of a mapping on Banach spaces and its applications. Fixed point theorems.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
Teaching methods
lectures and class exercises
Assessment methods
Exam: oral. Requirements: to manage the theory from lectures and exercises.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2013
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M7180/01: Wed 10:00–10:50 M3,01023, M. Čadek
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The aim of the course is to explain bases of theory of linear operators, spectral theory and theory of linear and nonlinear operator equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Integration of functions with values in Banach spaces. Bochner integral. Holomorphic functions with values in Banach spaces. Cauchy formula.
  • 2. Spectrum of linear operator. Classification of points of a spectrum. Spectral radius. Substitution of a bounded linear operator into functions holomorphic on its spectrum. Banach algebras.
  • 3. Spectral theory od selfadjoint and normal operators on Hilbert spaces.
  • 4. Application of spactral theory.
  • 5. Nonlinear functional analysis. Differential calculus on Banach spaces.
  • 6. Degree of a mapping on Banach spaces and its applications.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • Dunford, N. - Schwartz, T. Linear operators. Part I: General theory. New York and London: Interscience Publishers. XIV, 1958, 858 p.
  • ZEIDLER, Eberhard. Applied functional analysis : main principles and their applications. New York: Springer-Verlag, 1995, xvi, 404. ISBN 0387944222. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Teaching methods
lectures and class exercises
Assessment methods
Test during the semester. Examination: written and oral. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2011
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 17:00–18:50 M6,01011
  • Timetable of Seminar Groups:
M7180/01: Tue 19:00–19:50 M6,01011, A. Lomtatidze
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The aim of the course is to explain bases of theory of linear operators, spectral theory and theory of operator equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Linear operators. Definition and examples. Bounded and continuous operators. Inverse operators. Adjoint operators. Compact operators.
  • 2. Spectrum. Bases of the spectral analysis. Classification. Spectrum of the compact operator.
  • 3. Operator equations. Fredholm theory. Riesz-Schauder theory. Applications.
  • 4. Lerey-Schauder degree of mapping. Fixed point theorems. Solvabulity of nonlinear equations in Banach spaces.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • Dunford, N. - Schwartz, T. Linear operators. Part I: General theory. New York and London: Interscience Publishers. XIV, 1958, 858 p.
  • DRÁBEK, Pavel and Jaroslav MILOTA. Methods of nonlinear analysis : applications to differential equations. Basel: Birkhäuser, 2007, xii, 568. ISBN 9783764381462. info
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • ZEIDLER, Eberhard. Applied functional analysis : main principles and their applications. New York: Springer-Verlag, 1995, xvi, 404. ISBN 0387944222. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2009
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 16:00–17:50 M3,01023
  • Timetable of Seminar Groups:
M7180/01: Tue 18:00–18:50 M3,01023, A. Lomtatidze
Prerequisites
M6150 Linear Functional Analysis I
Differential and integral calculus, Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The aim of the course is to explain bases of theory of linear operators, spectral theory and theory of operator equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Linear operators. Definition and examples. Bounded and continuous operators. Inverse operators. Adjoint operators. Compact operators. 2. Spectrum. Bases of the spectral analysis. Classification. Spectrum of the compact operator. 3. Operator equations. Fredholm theory. Riesz-Schauder theory. Applications.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • Dunford, N. - Schwartz, T. Linear operators. Part I: General theory. New York and London: Interscience Publishers. XIV, 1958, 858 p.
  • ZEIDLER, Eberhard. Applied functional analysis : main principles and their applications. New York: Springer-Verlag, 1995, xvi, 404. ISBN 0387944222. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2007
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 13:00–14:50 UM
  • Timetable of Seminar Groups:
M7180/01: Tue 15:00–15:50 UM, A. Lomtatidze
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives (in Czech)
Cílem předmětu je seznámit posluchače s teorií lineárních operátorů, se základními pojmy spektrální analýzy a se základy teorie operátorových rovnic.
Syllabus (in Czech)
  • 1. Lineární operátory. Definice, příklady. Spojitost a ohraničenost. Invertovatelnost. Adjungované operátory. Adjungované operátory v unitárním prostoru. Kompaktní operátory. 2. Spektrum. Základní pojmy spektrální analýzy. Klasifikace bodů spektra. Spektrum kompaktního operátoru. 3. Operátorové rovnice. Fredholmové věty v Hilbertově prostoru. Ries-Schauderova teorie. Aplikace v teorii integrálních rovnic.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2005
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Mon 17:00–18:50 UP2
  • Timetable of Seminar Groups:
M7180/01: Mon 19:00–19:50 UP2, A. Lomtatidze
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives (in Czech)
Cílem předmětu je seznámit posluchače s teorií lineárních operátorů, se základními pojmy spektrální analýzy a se základy teorie operátorových rovnic.
Syllabus (in Czech)
  • 1. Lineární operátory. Definice, příklady. Spojitost a ohraničenost. Invertovatelnost. Adjungované operátory. Adjungované operátory v unitárním prostoru. Kompaktní operátory. 2. Spektrum. Základní pojmy spektrální analýzy. Klasifikace bodů spektra. Spektrum kompaktního operátoru. 3. Operátorové rovnice. Fredholmové věty v Hilbertově prostoru. Ries-Schauderova teorie. Aplikace v teorii integrálních rovnic.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2003
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable of Seminar Groups
M7180/01: No timetable has been entered into IS. A. Lomtatidze
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives (in Czech)
Cílem předmětu je seznámit posluchače s teorií lineárních operátorů, se základními pojmy spektrální analýzy a se základy teorie operátorových rovnic.
Syllabus (in Czech)
  • 1. Lineární operátory. Definice, příklady. Spojitost a ohraničenost. Invertovatelnost. Adjungované operátory. Adjungované operátory v unitárním prostoru. Kompaktní operátory. 2. Spektrum. Základní pojmy spektrální analýzy. Klasifikace bodů spektra. Spektrum kompaktního operátoru. 3. Operátorové rovnice. Fredholmové věty v Hilbertově prostoru. Ries-Schauderova teorie. Aplikace v teorii integrálních rovnic.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2001
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives (in Czech)
1.Spektrální teorie lineárních oprátorů - Základní pojmy spektrální analýzy z kursu LFA I - Klasifikace bodů spektra v konkrétních příkladech 2.Spektrální teorie kompaktních operátorů - Spektrální věta pro kompaktní operátory - Aplikace v teorii integrálních rovnic 3.Symetrické a samoadjungované operátory - Základní vlastnosti symetrických operátorů - Defektní čísla, samoadjungované rozšíření - Symetrické diferenciální operátory 4.Spektrální analýza samoadjungovaných operátorů - Spektrální věta 5.Diferenciální operátory - Singulární Sturm-Liouvilleův problém - LP/LC klasifikace
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 1999
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Syllabus (in Czech)
  • 1.Spektrální teorie lineárních oprátorů - Základní pojmy spektrální analýzy z kursu LFA I - Klasifikace bodů spektra v konkrétních příkladech 2.Spektrální teorie kompaktních operátorů - Spektrální věta pro kompaktní operátory - Aplikace v teorii integrálních rovnic 3.Symetrické a samoadjungované operátory - Základní vlastnosti symetrických operátorů - Defektní čísla, samoadjungované rozšíření - Symetrické diferenciální operátory 4.Spektrální analýza samoadjungovaných operátorů - Spektrální věta 5.Diferenciální operátory - Singulární Sturm-Liouvilleův problém - LP/LC klasifikace
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2024

The course is not taught in Autumn 2024

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Peter Šepitka, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005, 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1975, 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia, 1973, 408 s. URL info
Teaching methods
Lectures, seminars
Assessment methods
Two-hour written final exam (it is needed to reach at least 50 % of points) with oral evaluation of the exam with each student.
The conditions (especially regarding the form of the exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2022

The course is not taught in Autumn 2022

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005, 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1975, 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia, 1973, 408 s. URL info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2020

The course is not taught in Autumn 2020

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005, 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1975, 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia, 1973, 408 s. URL info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2018

The course is not taught in Autumn 2018

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005, 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002, 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1975, 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia, 1973, 408 s. URL info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2016

The course is not taught in Autumn 2016

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in this subject area; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Spectrum of linear operators (repetition from the course Functional analysis I).
  • 2. Spectral theory of self-adjoint and symmetric operators.
  • 3. Symmetric and self-adjoint operators in Hilbert spaces: Deficiency indices, self-adjoint extension of a symmetric operator.
  • 4. Differential calculus in Banach spaces.
  • 5. Strictly and uniformly convex spaces.
  • 6. Integration of functions with values in Banach spaces.
  • 7. Degree of a mapping on Banach spaces and its applications. Fixed point theorems.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
Teaching methods
lectures and class exercises
Assessment methods
Exam: oral. Requirements: to manage the theory from lectures and exercises.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2014

The course is not taught in Autumn 2014

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The aim of the course is to explain bases of theory of linear operators, spectral theory and theory of linear and nonlinear operator equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Integration of functions with values in Banach spaces. Bochner integral. Holomorphic functions with values in Banach spaces. Cauchy formula.
  • 2. Spectrum of linear operator. Classification of points of a spectrum. Spectral radius. Substitution of a bounded linear operator into functions holomorphic on its spectrum. Banach algebras.
  • 3. Spectral theory od selfadjoint and normal operators on Hilbert spaces.
  • 4. Application of spactral theory.
  • 5. Nonlinear functional analysis. Differential calculus on Banach spaces.
  • 6. Degree of a mapping on Banach spaces and its applications.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • Dunford, N. - Schwartz, T. Linear operators. Part I: General theory. New York and London: Interscience Publishers. XIV, 1958, 858 p.
  • ZEIDLER, Eberhard. Applied functional analysis : main principles and their applications. New York: Springer-Verlag, 1995, xvi, 404. ISBN 0387944222. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Teaching methods
lectures and class exercises
Assessment methods
Test during the semester. Examination: written and oral. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2012

The course is not taught in Autumn 2012

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The aim of the course is to explain bases of theory of linear operators, spectral theory and theory of operator equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Linear operators. Definition and examples. Bounded and continuous operators. Inverse operators. Adjoint operators. Compact operators.
  • 2. Spectrum. Bases of the spectral analysis. Classification. Spectrum of the compact operator.
  • 3. Operator equations. Fredholm theory. Riesz-Schauder theory. Applications.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • Dunford, N. - Schwartz, T. Linear operators. Part I: General theory. New York and London: Interscience Publishers. XIV, 1958, 858 p.
  • ZEIDLER, Eberhard. Applied functional analysis : main principles and their applications. New York: Springer-Verlag, 1995, xvi, 404. ISBN 0387944222. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2010

The course is not taught in Autumn 2010

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Linear Functional Analysis I
Differential and integral calculus, Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The aim of the course is to explain bases of theory of linear operators, spectral theory and theory of operator equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Linear operators. Definition and examples. Bounded and continuous operators. Inverse operators. Adjoint operators. Compact operators.
  • 2. Spectrum. Bases of the spectral analysis. Classification. Spectrum of the compact operator.
  • 3. Operator equations. Fredholm theory. Riesz-Schauder theory. Applications.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • Dunford, N. - Schwartz, T. Linear operators. Part I: General theory. New York and London: Interscience Publishers. XIV, 1958, 858 p.
  • ZEIDLER, Eberhard. Applied functional analysis : main principles and their applications. New York: Springer-Verlag, 1995, xvi, 404. ISBN 0387944222. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2008

The course is not taught in Autumn 2008

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Linear Functional Analysis I
Differential and integral calculus, Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The aim of the course is to explain bases of theory of linear operators, spectral theory and theory of operator equations.
Syllabus
  • 1. Linear operators. Definition and examples. Bounded and continuous operators. Inverse operators. Adjoint operators. Compact operators. 2. Spectrum. Bases of the spectral analysis. Classification. Spectrum of the compact operator. 3. Operator equations. Fredholm theory. Riesz-Schauder theory. Applications.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2006

The course is not taught in Autumn 2006

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives (in Czech)
Cílem předmětu je seznámit posluchače s teorií lineárních operátorů, se základními pojmy spektrální analýzy a se základy teorie operátorových rovnic.
Syllabus (in Czech)
  • 1. Lineární operátory. Definice, příklady. Spojitost a ohraničenost. Invertovatelnost. Adjungované operátory. Adjungované operátory v unitárním prostoru. Kompaktní operátory. 2. Spektrum. Základní pojmy spektrální analýzy. Klasifikace bodů spektra. Spektrum kompaktního operátoru. 3. Operátorové rovnice. Fredholmové věty v Hilbertově prostoru. Ries-Schauderova teorie. Aplikace v teorii integrálních rovnic.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2004

The course is not taught in Autumn 2004

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives (in Czech)
Cílem předmětu je seznámit posluchače s teorií lineárních operátorů, se základními pojmy spektrální analýzy a se základy teorie operátorových rovnic.
Syllabus (in Czech)
  • 1. Lineární operátory. Definice, příklady. Spojitost a ohraničenost. Invertovatelnost. Adjungované operátory. Adjungované operátory v unitárním prostoru. Kompaktní operátory. 2. Spektrum. Základní pojmy spektrální analýzy. Klasifikace bodů spektra. Spektrum kompaktního operátoru. 3. Operátorové rovnice. Fredholmové věty v Hilbertově prostoru. Ries-Schauderova teorie. Aplikace v teorii integrálních rovnic.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2000

The course is not taught in Autumn 2000

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives (in Czech)
1.Spektrální teorie lineárních oprátorů - Základní pojmy spektrální analýzy z kursu LFA I - Klasifikace bodů spektra v konkrétních příkladech 2.Spektrální teorie kompaktních operátorů - Spektrální věta pro kompaktní operátory - Aplikace v teorii integrálních rovnic 3.Symetrické a samoadjungované operátory - Základní vlastnosti symetrických operátorů - Defektní čísla, samoadjungované rozšíření - Symetrické diferenciální operátory 4.Spektrální analýza samoadjungovaných operátorů - Spektrální věta 5.Diferenciální operátory - Singulární Sturm-Liouvilleův problém - LP/LC klasifikace
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Linear Functional Analysis II

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives (in Czech)
Cílem předmětu je seznámit posluchače s teorií lineárních operátorů, se základními pojmy spektrální analýzy a se základy teorie operátorových rovnic.
Syllabus (in Czech)
  • 1. Lineární operátory. Definice, příklady. Spojitost a ohraničenost. Invertovatelnost. Adjungované operátory. Adjungované operátory v unitárním prostoru. Kompaktní operátory. 2. Spektrum. Základní pojmy spektrální analýzy. Klasifikace bodů spektra. Spektrum kompaktního operátoru. 3. Operátorové rovnice. Fredholmové věty v Hilbertově prostoru. Ries-Schauderova teorie. Aplikace v teorii integrálních rovnic.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2011 - acreditation

The course is not taught in Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The aim of the course is to explain bases of theory of linear operators, spectral theory and theory of operator equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Linear operators. Definition and examples. Bounded and continuous operators. Inverse operators. Adjoint operators. Compact operators.
  • 2. Spectrum. Bases of the spectral analysis. Classification. Spectrum of the compact operator.
  • 3. Operator equations. Fredholm theory. Riesz-Schauder theory. Applications.
Literature
  • Dunford, N. - Schwartz, T. Linear operators. Part I: General theory. New York and London: Interscience Publishers. XIV, 1958, 858 p.
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Applied functional analysis : main principles and their applications. New York: Springer-Verlag, 1995, xvi, 404. ISBN 0387944222. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.

M7180 Functional Analysis II

Faculty of Science
Autumn 2010 - only for the accreditation

The course is not taught in Autumn 2010 - only for the accreditation

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.
  • Enrolment Statistics (recent)