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线性偏微分算子分析 第2卷2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

线性偏微分算子分析 第2卷
  • （瑞典）赫尔曼德尔著 著
  • 出版社： 北京;西安：世界图书出版公司
  • ISBN：7519209278
  • 出版时间：2016
  • 标注页数：392页
  • 文件大小：46MB
  • 文件页数：402页
  • 主题词：

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图书目录

Introduction1

Chapter Ⅹ．Existence and Approximation of Solutions of Differential Equations3

Summary3

10.1．The Spaces Bp,k3

10.2．Fundamental Solutions16

10.3．The Equation P（D）u=f when f∈？′29

10.4．Comparison of Differential Operators32

10.5．Approximation of Solutions of Homogeneous Differential Equations39

10.6．The Equation P（D）u=f when f is in a Local Space ？′F41

10.7．The Equation P（D）u=f when f∈？′（X）45

10.8．The Geometrical Meaning of the Convexity Conditions50

Notes58

Chapter Ⅺ．Interior Regularity of Solutions of Differential Equations60

Summary60

11.1．Hypoelliptic Operators61

11.2．Partially Hypoelliptic Operators69

11.3．Continuation of Differentiability73

11.4．Estimates for Derivatives of High Order85

Notes92

Chapter Ⅻ．The Cauchy and Mixed Problems94

Summary94

12.1．The Cauchy Problem for the Wave Equation96

12.2．The Oscillatory Cauchy Problem for the Wave Equation104

12.3．Necessary Conditions for Existence and Uniqueness of Solutions to the Cauchy Problem110

12.4．Properties of Hyperbolic Polynomials112

12.5．The Cauchy Problem for a Hyperbolic Equation120

12.6．The Singularities of the Fundamental Solution125

12.7．A Global Uniqueness Theorem133

12.8．The Characteristic Cauchy Problem143

12.9．Mixed Problems162

Notes180

Chapter ⅩⅢ．Differential Operators of Constant Strength182

Summary182

13.1．Definitions and Basic Properties182

13.2．Existence Theorems when the Coefficients are Merely Continuous184

13.3．Existence Theorems when the Coefficients are in C∞186

13.4．Hypoellipticity191

13.5．Global Existence Theorems194

13.6．Non-uniqueness for the Cauchy Problem201

Notes224

Chapter ⅩⅣ．Scattering Theory225

Summary225

14.1．Some Function Spaces227

14.2．Division by Functions with Simple Zeros232

14.3．The Resolvent of the Unperturbed Operator237

14.4．Short Range Perturbations243

14.5．The Boundary Values of the Resolvent and the Point Spectrum251

14.6．The Distorted Fourier Transforms and the Continuous Spectrum255

14.7．Absence of Embedded Eigenvalues264

Notes268

Chapter ⅩⅤ．Analytic Function Theory and Differential Equations270

Summary270

15.1．The Inhomogeneous Cauchy-Riemann Equations271

15.2．The Fourier-Laplace Transform of Bc2,k（X）when X is Convex279

15.3．Fourier-Laplace Representation of Solutions of Differential Equations287

15.4．The Fourier-Laplace Transform of C？（X）when X is Convex296

Notes300

Chapter ⅩⅥ．Convolution Equations302

Summary302

16.1．Subharmonic Functions303

16.2．Plurisubharmonic Functions314

16.3．The Support and Singular Support of a Convolution319

16.4．The Approximation Theorem335

16.5．The Inhomogeneous Convolution Equation341

16.6．Hypoelliptic Convolution Equations353

16.7．Hyperbolic Convolution Equations356

Notes360

Appendix A．Some Algebraic Lemmas362

A.1．The Zeros of Analytic Functions362

A.2．Asymptotic Properties of Algebraic Functions of Several Variables364

Notes371

Bibliography373

Index391

Index of Notation392

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