Selected Topics in Functional Analysis

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Keywords:

Banach spaces, Hilbert spaces, Linear operators, Fourier transform, semigroups of operators

Requirements:

Basic course of Calculus and Linear Algebra (in the extent of the courses 01MA, 01MAA2-4, 01LAP, 01LAA2 held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Basic notions in topology and measure theory

2. Basic inequalities, convex functions

3. Banach spaces, spaces of bounded linear operators

4. Hilbert spaces, projectors, Radon-Nikodym theorem

5. Hahn-Banach theorem

6. Weak topology and convergence

7. Fourier transform and applications

8. Semigroups of operators

9. Applications in stochastic processes

Syllabus of tutorials:

Study Objective:

Ackquired knowledge::

Basic properties of linear operators in Banach and Hilbert spaces, meaning and use of Fourier transform.

Acquired skills:

Application of knowledge in particular examples.

Study materials:

Key references:

[1] Blank, Exner, Havlíček: Hilbert Space Operators in Quantum Physics, Springer, 2008.

Recommended references:

[2] M. Reed, B. Simon: Methods of Modern Mathematical Physics I.-IV., Academic Press, N. Zealand, 1972-1979

[3] Bobrowski: Functional Analysis for Probability and Stochastic Processes, An Introduction, New York, 2005

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: