NMMO302 Functional analysis for physicists

Link to SIS

Link to SIS [1]

Syllabus

Syllabus, general comments to the exam, literature SS 2021/2022

Lectures

1. Introduction.

2. Linear operators between Banach spaces; boundedness, examples and finite-dimensional vector spaces.

3. Seminorms and Frechet spaces. Hahn-Banach theorem.

4. Dual spaces. Reflexivity. Weak and weak-star convergences.

B. Baire's theorem.

5. Great theorems of LFA.

6. Adjoint operators. Compact operators.

7. Linear operators in Hilbert spaces. Riesz representation theorem.

8. Fredholm theory/Fredholm alternative.

9. Spectrum. An introduction to spectrum theory. 9. Spectrum focusing on Hilbert spaces over complex scalars.

A. Arzela-Ascoli theorem. (in czech)

C. Bases in vector spaces.

F. Abstract Fourier series. (in czech)

Recordings

Week 1 - L1 L2 L3

Week 2 - L4 L5

Week 3 - L6 L7 L8

Week 4 - L9 L10 L11

Week 6 - L12 L13 L14

Week 7 - L15 L16 L17 L18

Week 8 - L19 L20 L21

Week 9 - L22

Week 10 - L23 L24 L25

Week 11 - L28 L28 L28

Week 12 - L30 L30 L31

Week 13 - L33 L34 L35