中国美术年鉴

目录简介

《中国美术年鉴》.pdf电子版，共计406页，以下为本文献目录，仅供参考以实际为准。

1 1 What are Distributions?

1 1.1 Generalized functions and test functions

5 Contents

5 Preface

5 1.2 Examples of distributions

8 1.3 What good are distributions?

10 1.4 Problems

12 2 The Calculus of Distributions

12 2.1 Functions as distributions

14 2.2 Operations on distributions

18 2.3 Adioint identities

20 2.4 Consistency of derivatives

22 2.5 Distributional solutions of differential equations

25 2.6 Problems

28 3.1 From Fourier series to Fourier integrals

28 3 Fourier Transforms

31 3.2 The Schwartz class S

32 3.3 Properties of the Fourier transform on S

38 3.4 The Fourier inversion formula on S

41 3.5 The Fourier transform of a Gaussian

43 3.6 Problems

46 4 Fourier Transforms of Tempered Distributions

46 4.1 The definitions

49 4.2 Examples

55 4.3 Convolutions with tempered distributions

57 4.4 Problems

60 5　Solving Partial Differential Equations

60 5.1 The Laplace equation

64 5.2 The heat equation

67 5.3 The wave equation

72 5.4 Schr？dinger's equation and quantum mechanics

73 5.5 Problems

78 6　The Structure of Distributions

78 6.1 The support of a distribution

82 6.2　Structure theorems

85 6.3　Distributions with point support

88 6.4　Positive distributions

91 6.5 Continuity of distribution

98 6.6 Approximation by test functions

101 6.7　Local theory of distributions

103 6.8　Distributions on spheres

108 6.9　Problems

113 7 Fourier Analysis

113 7.1　The Riemann-Lebesgue lemma

119 7.2　Paley-Wiener theorems

125 7.3　The Poisson summation formula

130 7.4　Probability measures and positive definite functions

134 7.5　The Heisenberg uncertainty principle

139 7.6　Hermite functions

143 7.7 Radial Fourier transforms and Bessel functions

149 7.8　Haar functions and wavelets

157 7.9　Problems

162 8　Sobolev Theory and Microlocal Analysis

162 8.1 Sobolev inequalities

172 8.2 Sobolev spaces

176 8.3 Elliptic partial differential equations(constant coefficients)

185 8.4 Pseudodifferential operators

191 8.5 Hyperbolic operators

200 8.6 The wave front set

209 8.7 Microlocal analysis of singularities

214 8.8 Problems

219 Suggestions for Further Reading

221 Index