線性偏微分運算元分析 第1卷(第2版英文) ,

作者:L·赫爾曼德爾

出版社:世界圖書出版公司北京公司

ISBN:9787519209261

$31.50

產品號碼: 85735 貨號: 9787519209261 分類: , 標籤: , ,

本書作者是世界公認的數學分析領頭學者,這套4卷集的經典名著以廣義函數論為框架,論述了與偏微分方程理論有關的經典分析和現代分析的許多精華內容。第1卷重點論述分佈理論和傅立葉分析,特別是平穩方程和傅立葉奇異性分析,書中還有含提示和答案的習題,使本書更適合作為現代分析的研究生教材。

目錄

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

ChapterⅣ Convolution
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

ChapterⅤ Distributions in Product Spaces
Summary
5.1 Tensor Products
5.2 The Kernel Theorem
Notes

ChapterⅥ Composition 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

ChapterⅦ The 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

ChapterⅧ Spectral 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

ChapterⅨ Hyperfunctions
Summary
9.1.Analytic Functionals
9.2.General Hyperfunctions
9.3.The Analytic Wave Front Set ofa Hyperfunction
9.4.The Analytic Cauchy Problem
9.5.Hyperfunction Solutions of Partial Differential Equations
9.6.The Analytic Wave Front Set and the Support
Notes

Exercises
Answers and Hints to All the Exercises
Bibliography
Index
Index of Notation

作者介紹

赫爾曼德爾是米塔-列夫勒所奠定的瑞典分析學派的優秀繼承者,他的工作成果主要在現代線性偏微分方程理論方面。他是偽微分運算元和傅立葉積分運算元的奠基人之一。1959年,他在偏微分方程一般理論上取得了突破性成果。1962年,第14屆國際數學家大會在瑞典召開,赫爾曼德爾獲得了被譽為“數學界諾貝爾獎”的菲爾茲獎。

出版日期

05/01/2016

語系

簡體中文

版別

初版

裝訂

平裝

頁數

440

印刷

單色印刷

出版地

大陸