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中国美术年鉴PDF|Epub|txt|kindle电子书版本网盘下载
- 著
- 出版社： 上海市文化运动委员会
- ISBN：
- 出版时间：1948
- 标注页数：406页
- 文件大小：12MB
- 文件页数：236页
- 主题词：
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图书目录
1 What are Distributions?1
1.1 Generalized functions and test functions1
Contents5
Preface5
1.2 Examples of distributions5
1.3 What good are distributions?8
1.4 Problems10
2 The Calculus of Distributions12
2.1 Functions as distributions12
2.2 Operations on distributions14
2.3 Adioint identities18
2.4 Consistency of derivatives20
2.5 Distributional solutions of differential equations22
2.6 Problems25
3.1 From Fourier series to Fourier integrals28
3 Fourier Transforms28
3.2 The Schwartz class S31
3.3 Properties of the Fourier transform on S32
3.4 The Fourier inversion formula on S38
3.5 The Fourier transform of a Gaussian41
3.6 Problems43
4 Fourier Transforms of Tempered Distributions46
4.1 The definitions46
4.2 Examples49
4.3 Convolutions with tempered distributions55
4.4 Problems57
5 Solving Partial Differential Equations60
5.1 The Laplace equation60
5.2 The heat equation64
5.3 The wave equation67
5.4 Schr？dinger's equation and quantum mechanics72
5.5 Problems73
6 The Structure of Distributions78
6.1 The support of a distribution78
6.2 Structure theorems82
6.3 Distributions with point support85
6.4 Positive distributions88
6.5 Continuity of distribution91
6.6 Approximation by test functions98
6.7 Local theory of distributions101
6.8 Distributions on spheres103
6.9 Problems108
7 Fourier Analysis113
7.1 The Riemann-Lebesgue lemma113
7.2 Paley-Wiener theorems119
7.3 The Poisson summation formula125
7.4 Probability measures and positive definite functions130
7.5 The Heisenberg uncertainty principle134
7.6 Hermite functions139
7.7 Radial Fourier transforms and Bessel functions143
7.8 Haar functions and wavelets149
7.9 Problems157
8 Sobolev Theory and Microlocal Analysis162
8.1 Sobolev inequalities162
8.2 Sobolev spaces172
8.3 Elliptic partial differential equations(constant coefficients)176
8.4 Pseudodifferential operators185
8.5 Hyperbolic operators191
8.6 The wave front set200
8.7 Microlocal analysis of singularities209
8.8 Problems214
Suggestions for Further Reading219
Index221