线性偏微分算子分析（第三卷）（英文版）

本书共有4卷，作者是世界公认的分析学大师。这套4卷集的经典名著以广义函数论为框架，论述了与线性偏微分方程理论有关的经典分析和现代分析的核心内容。第2卷内容主要包括：微分方程解的存在性和近似性、微分方程解的内部正则性、柯西问题的混合边值问题、恒定强度的微分算子、散射理论、线性偏数方程的解析函数理论和卷积型方程等。

本书共有4卷，作者是世界公认的分析学大师。这套4卷集的经典名著以广义函数论为框架，论述了与线性偏微分方程理论有关的经典分析和现代分析的核心内容。第2卷内容主要包括：微分方程解的存在性和近似性、微分方程解的内部正则性、柯西问题的混合边值问题、恒定强度的微分算子、散射理论、线性偏数方程的解析函数理论和卷积型方程等。

Introduction
Chapter ⅩⅦ. Second Order Elliptic Operators
Summary
17.1. Interior Regularity and Local Existence Theorems
17.2. Unique Continuation Theorems
17.3. The Dirichlet Problem
17.4. The Hadamard Parametrix Construction
17.5. Asymptotic Properties of Eigenvalues and Eigenfunctions
Notes
Chapter ⅩⅧ. Pseudo-Differential Operators
Summary
18.1. The Basic Calculus
18.2. Conormal Distributions
18.3. Totally Characteristic Operators
18.4. Gauss Transforms Revisited
18.5. The Weyl Calculus
18.6. Estimates of Pseudo-Differential Operators
Notes
Chapter ⅩⅨ. Elliptic Operators on a Compact Manifold Without
Boundary
19.1. Abstract Fredholm Theory
19.2. The Index of Elliptic Operators
19.3. The Index Theorem in IRn
19.4. The Lefschetz Formula
19.5. Miscellaneous Remarks on Ellipticity
Notes
Chapter ⅩⅩ. Boundary Problems for Elliptic Differential Operators
Summary
20.1. Elliptic Boundary Problems
20.2. Preliminaries on Ordinary Differential Operators
20.3. The Index for Elliptic Boundary Problems
20.4. Non-Elliptic Boundary Problems
Notes
Chapter ⅩⅩⅠ. Symplectic Geometry
Summary
21.1. The Basic Structue
21.2. Submanifolds of a Sympletic Manifold
21.3. Normal Forms of Functions
21.4. Folds and Glancing Hypersufaces
21.5. Symplectic Equivalence of Quadratic Forms
21.6. The Lagrangian Grassmannian
Notes
Chapter ⅩⅩⅡ. Some Classes of （Micro-）hypoelliptic Operators
Chapter ⅩⅩⅢ. The Strictly hyperbolic Cauchy Problem
Chapter ⅩⅩⅣ. The Mixed Dirichlet-Cauchy Prblem for Second Order Operators
Appendix B. Some Spaces of Distributions
Appendix C. Some Tools from Differential Geometry
Bibliography
Index
Index of Notation

The first two volumes of this monograph can be regarded as an expansion and updating of my book "Linear partial differential operators" published in the Grundlehren series in 1963. However, volumes III and IV are almost entirely new. In fact they are mainly devoted to the theory of linear differential operators as it has developed after 1963. Thus the main topics are pseudo-differential and Fourier integral operators with the underlying symplectic geometry. The contents will be discussed in greater detail in the introduction. I wish to expr..