出版时间:2005-6 出版社:世图 作者:L.Hormander 页数:524
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内容概要
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。
书籍目录
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 NotesChapter 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 NotesChapter 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 NotesChapter ⅩⅩⅡ. Some Classes of (Micro-)hypoelliptic OperatorsChapter ⅩⅩⅢ. The Strictly hyperbolic Cauchy ProblemChapter ⅩⅩⅣ. The Mixed Dirichlet-Cauchy Prblem for Second Order OperatorsAppendix B. Some Spaces of DistributionsAppendix C. Some Tools from Differential GeometryBibliographyIndexIndex of Notation
编辑推荐
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。
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