No. | Date. | Notes. |
Part 1. An Introduction to Non-harmonic Fourier Analysis
|
Lecture 1
|
2023/02/14
| Lecture 1: Chapter 1: Bases in Banach Spaces-Schauder basis, Schauder
theorem and Orthonormal basis in Hilbert Space |
Lecture 2 | 2023/02/16 | Lecture 2: cont.Hilbert Space, Reproducing Kernel |
Lecture 3
| 2023/02/23 | Lecture 3: Complete sequences, Coefficient functional, Riesz basis |
Lecture 4
|
2023/02/28
| Lecture 4: cont. Equivalent condition of Riesz basis, Paley-wiener
criterion |
Lecture 5
| 2023/03/02 | Lecture 5: Problem Set Discussion-1, Chapter 2: Entire functions of
Exponential Type 这一个Lecture和之后的Lecture有部分Complex Analysis的内容 |
Lecture 6
|
2023/03/09
| Lecture 6: cont. Entire function of exponential type |
Lecture 7 | 2023/03/14 | Lecture 7: Paley-Wiener Theorem and Paley-Wiener space |
Lecture 8 | 2023/03/16 | Lecture 8: Chapter 3: The Completeness of sets of complex exponentials |
Lecture 9 | 2023/03/23 | Lecture 9: cont.Completeness of sets of complex exponentials, Kadec 1/4 theorem |
Lecture 10 |
2023/03/28
| Lecture 10: Stability, Chapter 4: Interpolation and basis in Hilbert space |
Lecture 11 | 2023/03/30 | Lecture 11: cont.Bessel Sequences, Riesz-Fischer Sequences, Moment Space and Equivalent Sequences,
Frame |
Lecture 12
|
2023/04/06
| Lecture 12: cont. Exact frame and Riesz basis, Stability of Non-harmonic
Series |
Part 2: A Course in Abstract Harmonic Analysis
(🗒️ Outline) |
Lecture 13
|
2023/04/11
| |
Lecture 14
| 2023/04/13 | Lecture 14: p-adic field Qp |
Lecture 15 | 2023/04/20 | Lecture 15: Convolutions on G, Homogeneous spaces |
Lecture 16 | 2023/04/25 | Lecture 16: Banach Algebra and Basic Representation Theory |
Lecture 17 | 2023/04/27 | Lecture 17: cont. Basic Representation Theory |
Lecture 18 | 2023/05/04 | Lecture 18: Analysis on locally compact abelian groups |
Lecture 19 | 2023/05/09 | Lecture 19: cont. Characters |
Lecture 20 | 2023/05/11 | Lecture 20: Qp hat sim Qp, Fourier Transform |
Lecture 21 | 2023/05/18 | Lecture 21: Bochner’s theorem, Fourier Inversion |
Lecture 22 | 2023/05/23 | Lecture 22: Pontrjagin Duality |
Lecture 23 | 2023/05/25 | Lecture 23: Proof of Pontrjagin Duality, Poisson Summation Formula |
Lecture 24 | 2023/06/01 | Lecture 24: cont. Poisson Summation Formula |