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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2011/2012

Selected topics in functional analysis

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Code Completion Credits Range
01VPFA Z,ZK 3 2+1
Lecturer:
Miloslav Havlíček (gar.), Severin Pošta
Tutor:
Miloslav Havlíček (gar.), Severin Pošta
Supervisor:
Department of Mathematics
Synopsis:

Selected topics in functional analysis, functional analysis methods used in probability, statistics and stochastic processes.

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:

1. Elements of topology, measure theory, convex functions and basic inequalities

2. Properties of Banach and Hilbert spaces

3. Bounded linear operators

4. Fourierova transform

5. Complete orthonormal systems in Hilbert spaces

6. Weak convergence

7. Semigroups, Markov processes

Study Objective:

Basic skills for applications in probability, statistics and stochastic processes.

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:
Time-table for winter semester 2011/2012:
Time-table is not available yet
Time-table for summer semester 2011/2012:
Time-table is not available yet
The course is a part of the following study plans:
Generated on 2012-7-9
For updated information see http://bilakniha.cvut.cz/en/predmet1916506.html