斯克利普斯学院 泛函分析与调和分析 (Scripps College, Basic Functional and Harmonic Analysis)

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2018-12-26 22:45:23
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https://www.youtube.com/playlist?list=PLun8-Z_lTkC6x1sq8fRpuQAvIz2rK9xFb 讲师:Winston Ou 公开课目录:https://zhuanlan.zhihu.com/p/53069070
视频选集
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01 - Banach Spaces; L^p spaces
53:41
02 - L^p spaces are complete; Dual spaces
01:11:36
03 - Dual Banach Spaces
01:04:55
04 - Dual L^p spaces
01:07:28
05 - Hahn-Banach Theorem and Applications
01:04:48
06 - Riesz Interpolation Theorem, Part I
01:05:55
07 - Riesz Interpolation Theorem, Part II
01:10:46
08 - The Hilbert Transform
01:06:37
09 - L^p boundedness of the Hilbert Transform
01:00:37
10 - L^p boundedness of the Maximal Function
01:13:14
11 - L^p functions of bounded support in Hardy space
01:10:18
12 - Boundedness of Hilbert Transform on Hardy Space, Part I
01:10:46
13 - Boundedness of Hilbert Transform on Hardy Space, Part II
01:11:48
14 - BMO is the dual of H^1; Distributions
01:14:12
15 - Operations on Distributions; Tempered distributions
01:13:50
16 - Tempered Distributions
01:06:24
17 - Convolution and the Fourier Transform; p.v. (1/x)
01:09:41
18 - Fundamental Solution of the Heat Operator
01:05:28
19 - Elliptic operators and regular parametrices
01:11:03
20 - L^p boundedness of Singular Integrals
01:14:02
21 - L^p boundedness of Singular Integrals, ct’d
01:00:07
22 - L^p boundedness of Singular Integrals, end; Baire Category
01:10:49
23 - Applications of the Baire Category Theorem
01:12:16
24 - More applications of the Baire Category Theorem
01:13:35
25 - Closed Graph Theorem, Besicovitch Sets
44:48
26 - Besicovitch sets are generic
01:10:36
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