線(xiàn)性偏微分算子分析 第3卷

內(nèi)容概要

　　本書(shū)共有4卷，作者是世界公認(rèn)的分析學(xué)大師。這套4卷集的經(jīng)典名著以廣義函數(shù)論為框架，論述了與線(xiàn)性偏微分方程理論有關(guān)的經(jīng)典分析和現(xiàn)代分析的核心內(nèi)容。第2卷內(nèi)容主要包括：微分方程解的存在性和近似性、微分方程解的內(nèi)部正則性、柯西問(wèn)題的混合邊值問(wèn)題、恒定強(qiáng)度的微分算子、散射理論、線(xiàn)性偏數(shù)方程的解析函數(shù)理論和卷積型方程等。

書(shū)籍目錄

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

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本書(shū)共有4卷，作者是世界公認(rèn)的分析學(xué)大師。這套4卷集的經(jīng)典名著以廣義函數(shù)論為框架，論述了與線(xiàn)性偏微分方程理論有關(guān)的經(jīng)典分析和現(xiàn)代分析的核心內(nèi)容。第2卷內(nèi)容主要包括：微分方程解的存在性和近似性、微分方程解的內(nèi)部正則性、柯西問(wèn)題的混合邊值問(wèn)題、恒定強(qiáng)度的微分算子、散射理論、線(xiàn)性偏數(shù)方程的解析函數(shù)理論和卷積型方程等。

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