拟微分和奇异积分算子
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作者(德)A.埃布尔斯
出版社世界图书出版公司
ISBN9787519214746
出版时间2016-12
版次1
装帧平装
开本16开
纸张胶版纸
页数222页
字数99999千字
定价58元
上书时间2024-08-02
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基本信息
书名:拟微分和奇异积分算子
定价：58.00元
作者:(德)A.埃布尔斯
出版社：世界图书出版公司
出版日期：2016-12-01
ISBN：9787519214746
字数：278000
页码：222
版次：1
装帧：平装
开本：16开
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内容提要
《拟微分和奇异积分算子》 自成一体，全面介绍了拟微分算子和奇异积分算子理论，给出了椭圆及抛物线方程应用，讨论了函数空间理论。该书由三部分组成。部分主要是傅立叶变换和增缓广义函数及拟微分算子。第二部分主要介绍奇异积分算子。第三部分主要涉及前两部分理论的应用。目次：序言介绍；傅立叶变换和拟微分算子；傅立叶变换和缓增广义函数；Rn拟微分算子的基本计算；奇异积分算子，平移不变的奇异积分算子；非平移
目录
Preface1 IntroductionⅠ Fourier Transformation and Pseudodifferential OperatorsFourier Transformation and Tempered Distributions2.1 Definition and Basic Properties2.2 Rapidly Decreasing Functions—8（Rn）2.3 Inverse Fourier Transformation and Plancherels Theorem2.4 Tempered Distributions and Fourier Transformation2.5 Fourier Transformation and Convolution of Tempered Distributions2.6 Convolution on δ（Rn）and Fundamental Solutions2.7 Sobolev and Bessel Potential Spaces2.8 Vector—Valued Fourier—Transformation2.9 Final Remarks and Exercises2.9.1 Further Reading2.9.2 Exercises3 Basic Calculus of Pseudodifferential Operators on Rn3.1 Symbol Classes and Basic Properties3.2 Composition of Pseudodifferential Operators： Motivation3.3 Oscillatory Integrals3.4 Double Symbols3.5 Composition of Pseudodifferential Operators3.6 Application： Elliptic Pseudodifferential Operators and Parametrices3.7 Boundedness on C∞b（Rn）and Uniqueness of the Symbol3.8 Adjoints of Pseudodifferential Operators and Operators in（x，y）—Form3.9 Boundedness on L2（Rn）and L2—Bessel Potential Spaces3.10 Outlook： Coordinate Transformations and PsDOs on Manifolds3.11 Final Remarks and Exercises3.11.1 Further Reading3.11.2 ExercisesⅡ Singular Integral Operators4 Translation Invariant Singular Integral Operators4.1 Motivation4.2 Main Result in the Translation Invariant Case4.3 Calder6n—Zygmund Decomposition and the Maximal Operator4.4 Proof of the Main Result in the Translation Invariant Case4.5 Examples of Singular Integral Operators4.6 Mikhlin Multiplier Theorem4.7 Outlook： Hardy spaces and BMO4.8 Final Remarks and Exercises4.8.1 Further Reading4.8.2 ExercisesNon—Translation Invariant Singular Integral Operators5.1 Motivation5.2 Extension to Non—Translation Invariant and Vector—Valued SingularIntegral Operators5.3 Hilbert—Space—Valued Mikhlin Multiplier Theorem5.4 Kernel Representation of a Pseudodifferential Operator5.5 Consequences of the Kernel Representation5.6 Final Remarks and Exercises5.6.1 Further Reading5.6.2 ExercisesⅢ Applications to Function Space and Differential Equations6 Introduction to Besov and Bessel Potential Spaces6.1 Motivation6.2 A Fourier—Analytic Characterization of Holder Continuity6.3 Bessel Potential and Besov Spaces—Definitions and Basic Properties6.4 Sobolev Embeddings6.5 Equivalent Norms6.6 Pseudodifferential Operators on Besov Spaces6.7 Final Remarks and Exercises6.7.1 Further Reading6.7.2 Exercises7 Applications to Elliptic and Parabolic Equations7.1 Applications of the Mikhlin Multiplier Theorem7.1.1 Resolvent of the Laplace Operator7.1.2 Soectrum of Multiolier Ooerators with Homogeneous Symbols7.1.3 Spectrum of a Constant Coefficient Differential Operator7.2 Applications of the Hilbert—Space—Valued Mikhlin Multiplier Theorem7.2.1 Maximal Regularity of Abstract ODEs in Hilbert Spaces7.2.2 Hilbert—Space Valued Bessel Potential and Sobolev Spaces7.3 Applications of Pseudodifferential Operators7.3.1 Elliptic Regularity for Elliptic Pseudodifferential Operators7.3.2 Resolvents of Parameter—Elliptic Differential Operators7.3.3 Application of Resolvent Estimates to Parabolic Initial Value Problems7.4 Final Remarks and Exercises7.4.1 Further Reading7.4.2 ExercisesⅣ AppendixA Basic Results from AnalysisA.1 Notation and Functions on RnA.2 Lebesgue Integral and LP—SpacesA.3 Linear Operators and Dual SpacesA.4 Bochner Integral and Vector—Valued LP—SpacesA.5 Frechet SpacesA.6 ExercisesBibliographyIndex
作者介绍
Helmut Abels（A.埃布尔斯）是德国公立大学雷根斯堡大学（Universitat Regenurg）本书自成一体，可作为研究生教材。
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