《線性偏微分運算元分析·第2卷》是2016年世界圖書出版公司出版的著作，作者是[瑞典] Lars Hormander（L.赫爾曼德爾）。
基本介紹
- 書名：《線性偏微分運算元分析·第2卷》
- 作者：[瑞典] Lars Hormander（L.赫爾曼德爾）
- 出版社：世界圖書出版公司
- 出版時間：2016年11月01日
內容簡介,作者簡介,目錄 ,
內容簡介
本書作者是世界公達獄喇乎認的數學分析領頭學者，這套4卷集的經典名著以廣義函式論為框架，論述了與偏奔定墓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2卷目次：微分方程解的存在性和近似請棄性；微分方程解的內部陵詢葛正則性；柯西問題和混合問題；恆定強度的微分運算元；散射理蒸詢請甩論；解析函式理論和微虹獄應分程；卷積方程。
作者簡介
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雅協店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。
目錄
Introduction
Chapter 10.Existence and Approximation of Solutions of
Differential Equations
Summary
10.1.The Spaces Bp.k
10.2.Fundamental Solutions
10.3.The Equation P（D） u =f when
10.4.Comparison of Differential Operators
10.5.Approximation of Solutions of Homogeneous Differential Equations
10.6.The Equation P（D）u=f when f is in a Local Space
10.7.The Equation P（D） u =f when
10.8.The Geometrical Meaning of the Convexity Conditions
Notes
Chapter 11.Interior Regularity of Solutions of Differential Equations
Summary
11.1.HypoeUiptic Operators
11.2.Partially Hypoelliptic Operators
11.3.Continuation of Differentiability
11.4.Estimates for Derivatives of High Order
Notes
Chapter 12.The Cauchy and Mixed Problems
Summary
12.1.The Cauchy Problem for the Wave Equation
12.2.The Oscillatory Cauchy Problem for the Wave Equation
12.3.Necessary Conditions for Existence and Uniqueness of Solutions to the Cauchy Problem
12.4.Properties of Hyperbolic Polynomials
12.5.The Cauchy Problem for a Hyperbolic Equation
12.6.The Singularities of the Fundamental Solution
12.7.A Global Uniqueness Theorem
12.8.The Characteristic Cauchy Problem
Chapter 13.Differential Operators of Constant Strenath
13.1.Definitions and Basic Properties
13.2.Existence Theorems when the Coefficients are Merely Continuous
13.3.Existence Theorems when the Coefficients are in C∞
13.4.Hypoellipticity
13.5.Global Existence Theorems
13.6.Non—uniqueness for the Cauchy Problem
Chapter 14.Scattering Theory
14.1.Some Function Spaces
14.2.Division by Functions with Simple Zeros
14.3.The Resolvent of the Unperturbed Operator
14.4.Short Range Perturbations
14.5.The Boundary Values of the Resolvent and the Point Spectrum
14.6.The Distorted Fourier Transforms and the Continuous Spectrum
14.7.Absence of Embedded Eigenvalues
Notes
Chapter 15.Analytic Function Theory and Differential Equations
Summary
15.1.The Inhomogeneous Cauchy—Riemann Equations
15.2.The Fourier—Laplace Transform of （X） when X is Convex
15.3.Fourier—Laplace Representation of Solutions of Differential Equations
15.4.The Fourier—Laplace Transform of C∞0（X） when X is Convex
Notes
Chapter 16.Convolution Equations
Summary
16.1.Subharmonic Functions
16.2.Plurisubharmonic Functions
16.3.The Support and Singular Support of a Convolution
16.4.The Approximation Theorem
16.5.The Inhomogeneous Convolution Equation
16.6.Hypoelliptic Convolution Equations
16.7.Hyperbolic Convolution Equations
Notes
Appendix A.Some Algebraic Lemmas
A.1.The Zeros of Analytic Functions
A.2.Asymptotic Properties of Aloebraic Functions of Several Variables
Notes
Bibliography
Index
Index of Notation
12.3.Necessary Conditions for Existence and Uniqueness of Solutions to the Cauchy Problem
12.4.Properties of Hyperbolic Polynomials
12.5.The Cauchy Problem for a Hyperbolic Equation
12.6.The Singularities of the Fundamental Solution
12.7.A Global Uniqueness Theorem
12.8.The Characteristic Cauchy Problem
Chapter 13.Differential Operators of Constant Strenath
13.1.Definitions and Basic Properties
13.2.Existence Theorems when the Coefficients are Merely Continuous
13.3.Existence Theorems when the Coefficients are in C∞
13.4.Hypoellipticity
13.5.Global Existence Theorems
13.6.Non—uniqueness for the Cauchy Problem
Chapter 14.Scattering Theory
14.1.Some Function Spaces
14.2.Division by Functions with Simple Zeros
14.3.The Resolvent of the Unperturbed Operator
14.4.Short Range Perturbations
14.5.The Boundary Values of the Resolvent and the Point Spectrum
14.6.The Distorted Fourier Transforms and the Continuous Spectrum
14.7.Absence of Embedded Eigenvalues
Notes
Chapter 15.Analytic Function Theory and Differential Equations
Summary
15.1.The Inhomogeneous Cauchy—Riemann Equations
15.2.The Fourier—Laplace Transform of （X） when X is Convex
15.3.Fourier—Laplace Representation of Solutions of Differential Equations
15.4.The Fourier—Laplace Transform of C∞0（X） when X is Convex
Notes
Chapter 16.Convolution Equations
Summary
16.1.Subharmonic Functions
16.2.Plurisubharmonic Functions
16.3.The Support and Singular Support of a Convolution
16.4.The Approximation Theorem
16.5.The Inhomogeneous Convolution Equation
16.6.Hypoelliptic Convolution Equations
16.7.Hyperbolic Convolution Equations
Notes
Appendix A.Some Algebraic Lemmas
A.1.The Zeros of Analytic Functions
A.2.Asymptotic Properties of Aloebraic Functions of Several Variables
Notes
Bibliography
Index
Index of Notation
