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PřF:M7180 Linear Functional Analysis II - Course Information

## 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:

*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, 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**- 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.

- Enrolment Statistics (Autumn 2009, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2009/M7180