Selected Topics in Functional Analysis
Code  Completion  Credits  Range  Language 

01VPF  Z,ZK  4  2+2  Czech 
 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, 01MAA24, 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, RadonNikodym theorem
5. HahnBanach 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, 19721979
[3] Bobrowski: Functional Analysis for Probability and Stochastic Processes, An Introduction, New York, 2005
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: