Лекции

1

Lecture 1. Basics of Functional Analysis. Metric Spaces

01:33:50

2

Lecture 2. Metric Spaces. Normed Spaces. Seminorms and Polynormed Spaces. Banach Spaces

01:31:24

3

Lecture 3. Euclidean and Hilbert Spaces

01:37:15

4

Lecture 4. Separable Hilbert Spaces. Bases in Hilbert Spaces

01:18:25

5

Lecture 5. Compact and Precompact Sets in Metric Spaces

01:22:51

6

Lecture 6. Compact and Precompact Sets: Exercises

01:24:49

7

Lecture 7. Linear Operators and Functionals in Normed Spaces

01:25:57

8

Lecture 8. Linear Operators and Functionals in Normed Spaces: Exercises

01:19:08

9

Lecture 9. The Hahn–Banach Theorem and the Corollaries

01:26:33

10

Lecture 10. (C[a,b])*. Norms of Functionals

01:29:41

11

Lecture 11. Hilbert Space Duality. Modes of Convergence

01:28:04

12

Lecture 12. Reproducing Kernels and Weak Convergence: Exercises

01:29:06

13

Lecture 13. Adjoint, Self-Adjoint, and Normal Operators. Hellinger–Toeplitz Theorem

01:55:20

14

Lecture 14. Adjoint Operators: Exercises

01:00:13

15

Lecture 15. Compact Operators. Inverse Operator

01:33:14

16

Lecture 16. Exercises on Compact and Inverse Operators

01:21:54

17

Lecture 17. Spectrum of a Bounded Operator. Classification of Points in the Spectrum

01:33:59

18

Lecture 18. Exercises on Spectra of Operators

01:30:59

19

Lecture 19. The Hilbert–Schmidt Theorem

01:40:43

20

Lecture 20. Applications of the Hilbert–Schmidt Theorem

01:20:46

21

Lecture 21. Fredholm Theory

01:31:07

22

Lecture 22. Fredholm Theory: Exercises

01:26:41

23

Lecture 23. Unbounded Operators: Introduction

01:33:20

24

Lecture 24. Symmetric Operators

01:25:38

25

Lecture 25. Isometric Operators and the Cayley Transform. Self-Adjoint Extensions of Symmetric Operators

01:36:28

26

Lecture 26. Functional Calculus

01:32:56

27

Lecture 27. Spectral Theorem for Self-Adjoint Operators. Fourier Transform in L₁

01:28:44

28

Lecture 28. Fourier Transform in L₁, S, and L₂

01:28:41

29

Lecture 29. Test Functions and Distributions

01:23:06

30

Lecture 30. Convolution

01:20:04