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PřF:M7180 Functional Analysis II - Course Information

## 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:

*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**- Algebra and Discrete Mathematics (programme PřF, N-MA)
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Statistics and Data Analysis (programme PřF, N-MA)

**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, A. N. and S. V. FOMIN.
*Základy teorie funkcí a funkcionální analýzy*. 1. vyd. 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.

- Enrolment Statistics (Autumn 2013, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2013/M7180