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. xi, 353. ISBN 8086843009. 2004. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství. 215 s. 1986. 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.
  • Enrolment Statistics (Autumn 2015, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2015/M7180