拟微分和奇异积分算子(英文版)
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作者(德)埃布尔斯
出版社世界图书出版公司
ISBN9787519214746
出版时间2016-07
装帧其他
开本其他
定价58元
货号3718346
上书时间2024-06-11
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目录
Preface
1 Introduction
Ⅰ Fourier Transformation and Pseudodifferential Operators
2 Fourier Transformation and Tempered Distributions
2.1 Definition and Basic Properties
2.2 Rapidly Decreasing Functions - 8(Rn)
2.3 Inverse Fourier Transformation and Plancherel's Theorem
2.4 Tempered Distributions and Fourier Transformation
2.5 Fourier Transformation and Convolution of Tempered Distributions.
2.6 Convolution on 8'(Rn) and Fundamental Solutions
2.7 Sobolev and Bessel Potential Spaces
2.8 Vector-Valued Fourier-Transformation
2.9 Final Remarks and Exercises
2.9.1 Further Reading
2.9.2 Exercises
3 Basic Calculus of Pseudodifferentiai Operators on Rn
3.1 Symbol Classes and Basic Properties
3.2 Composition of Pseudodifferential Operators: Motivation
3.3 Oscillatory Integrals
3.4 Double Symbols
3.5 Composition of Pseudodifferential Operators
3.6 Application: Elliptic Pseudodifferential Operators and Parametrices.
3.7 Boundedness on C∞/b(Rn) and Uniqueness of the Symbol
3.8 Adjoints of Pseudodifferential Operators and Operators in (x, y)-Form
3.9 Boundedness on L2(Rn) and L2-Bessel Potential Spaces
3.1 0 Outlook: Coordinate Transformations and PsDOs on Manifolds
3.1 1 Final Remarks and Exercises
3.1 1.1 Further Reading
3.1 1.2 Exercises
Ⅱ Singular Integral Operators
4 Translation Invariant Singular Integral Operators
4.1 Motivation
4.2 Main Result in the Translation Invariant Case
4.3 Calder6n-Zygmund Decomposition and the Maximal Operator
4.4 Proof of the Main Result in the Translation Invariant Case
4.5 Examples of Singular Integral Operators
4.6 Mikhlin Multiplier Theorem
4.7 Outlook: Hardy spaces and BMO
4.8 Final Remarks and Exercises
4.8.1 Further Reading
4.8.2 Exercises
5 Non-Translation Invariant Singular Integral Operators
5.1 Motivation
5.2 Extension to Non-Translation Invariant and Vector-Valued Singular Integral Operators
5.3 Hilbert-Space-Valued Mikhlin Multiplier Theorem
5.4 Kernel Representation of a Pseudodifferential Operator
5.5 Consequences of the Kernel Representation
5.6 Final Remarks and Exercises
5.6.1 Further Reading
5.6.2 Exercises
Ⅲ Applications to Function Space and Differential Equations
6 Introduction to Besov and Bessel Potential Spaces
6.1 Motivation
6.2 A Fourier-Analytic Characterization of Ho1der Continuity
6.3 Bessel Potential and Besov Spaces - Definitions and Basic Properties
6.4 Sobolev Embeddings
6.5 Equivalent Norms
6.6 Pseudodifferential Operators on Besov Spaces
6.7 Final Remarks and Exercises
6.7.1 Further Reading
6.7.2 Exercises
7 Applications to Elliptic and Parabolic Equations
7.1 Applications of the Mikhlin Multiplier Theorem
7.1.1 Resolvent of the Laplace Operator
7.1.2 Spectrum of Multiplier Operators with Homogeneous Symbols
7.1.3 Spectrum of a Constant Coefficient Differential Operator
7.2 Applications of the Hilbert-Space-Valued Mikhlin Multiplier Theorem
7.2.1 Maximal Regularity of Abstract ODEs in Hilbert Spaces
7.2.2 Hilbert-Space Valued Bessel Potential and Sobolev Spaces
7.3 Applications of Pseudodifferential Operators
7.3.1 Elliptic Regularity for Elliptic Pseudodifferential Operators
7.3.2 Resolvents of Parameter-Elliptic Differential Operators
7.3.3 Application of Resolvent Estimates to Parabolic Initial Value Problems
7.4 Final Remarks and Exercises
7.4.1 Further Reading
7.4.2 Exercises
Ⅳ Appendix
A Basic Results from Analysis
A.1 Notation and Functions on Rn
A.2 Lebesgue Integral and LP-Spaces
A.3 Linear Operators and Dual Spaces
A.4 Bochner Integral and Vector-Valued LP-Spaces
A.5 Frechet Spaces
A.6 Exercises
Bibliography
Index
内容摘要
埃布尔斯著的《拟微分和奇异积分算子(英文版)》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。第一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
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