线性偏微分算子分析 第1卷（英文版） 目录

Introduction
ChapterⅠ Test Functions
Summary
1.1 A review of Differential Calculus
1.2 Existence of Test Functions
1.3 Convolution
1.4 Cutoff Functions and Partitions of Unity
Notes
ChapterⅡ Definition and Basic Properties of Distributions
Summary
2.1 Basic Definitions
2.2 Localization
2.3 Distributions with Compact Support
Notes
ChapterⅢ Differentiation and Multiplication by Functions
Summary
3.1 Definition and Examples
3.2 Homogeneous Distributions
3.3 Some Fundamental Solutions
3.4 Evaluation of Some Integrals
Notes
ChapterⅣConvolution
Summary
4.1 Convolution with a Smooth Function
4.2 Convolution of Distributions
4.3 The Theorem of Supports
4.4 The Role of Fundamental Solutions
4.5 Basic Lp Estimates for Convolutions
Notes
ChapterⅤDistributions in Product Spaces
Summary
5.1 Tensor Products
5.2 The Kernel Theorem
Notes
ChapterⅥComposition with Smooth Maps
Summary
6.1 Definitions
6.2 Some Fundamental Solutions
6.3 Distributions on a Manifold
6.4 The Tangent and Cotangent Bundles
Notes
ChapterⅦThe Fourier Transformation
Summary
7.1 The Fourier Transformation in and in
7.2 Poissons Summation Formula and Periodic Distributions
7.3 The Fourier-Laplace Transformation in
7.4 More General Fourier-Laplace Transforms
7.5 The Malgrange Preparatio Theorem
7.6 Fourier Transforms of Gaussian Functions
7.7 The Method of Stationary Phase
7.8 Oscillatory Integrals
7.9 H(s)Lp and Holder Estimates
Notes
ChapterⅧSpectral Analysis of Singularities
Summary
8.1 The Wave Front Set
8.2 A Review of Operations with Distributions
8.3 The Wave Front Set of Solutions Of Partial Differential Equations
8.4 THe Wave Front Set With Respect to
8.5 Rules of Computation for WFL
8.6 WFL for Solutions of Partial Differential Equations
8.7 Microhyperbolicity
Notes
ChapterⅨHyperfunctions
Summary
……
Exercises
Answers and Hints to All the Exercises
Bibliography
Index
Index of Notation

线性偏微分算子分析 第1卷（英文版） 内容简介

本书作者是世界公认的数学分析领头学者，这套4卷集的经典名著以广义函数论为框架，论述了与偏微分方程理论有关的经典分析和现代分析的许多精华内容。第1卷重点论述分布理论和傅立叶分析，特别是平稳方程和傅立叶奇异性分析，书中还有含提示和答案的习题，使本书更适合作为现代分析的研究生教材。第1卷目次：测试函数；广义函数的定义和基本性质；广义函数的微分及乘以函数；卷积；积空间中的广义函数；带有光滑映象的复合；傅立叶变换；奇点的谱分析；超函数。