调和分析概览（影印版）
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库存27件
广东广州
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作者Steven G. Krantz
出版社高等教育出版社
ISBN9787040570274
出版时间2022-02
装帧平装
开本其他
定价169元
货号29376572
上书时间2024-11-03
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导语摘要
本书介绍了调和分析，从其早的开端到的研究进展。遵循历史和概念的起源，本书讨论了单变量和多变量的傅里叶级数、傅里叶变换、球面调和函数、分数次积分、欧氏空间上的奇异积分。从齐性空间的角度来考虑早期观点是本书的精彩之处。书末讨论了小波，它是调和分析中的思想之一。 本书适合研究生、高年级本科生、数学家和任何想快速纵览调和分析的人阅读，读者所需的背景知识包括微积分、集合论、积分理论、序列和级数理论。
目录
Preface
0 Overview of Measure Theory and Functional Analysis
0.1 Pre-Basics
0.2 A Whirlwind Review of Measure Theory
0.3 The Elements of Banach Space Theory
0.4 Hilbert Space
0.5 Two Fundamental Principles of Functional Analysis
1 Fourier Series Basics
1.0 The Pre-History of Fourier Analysis
1.1 The Rudiments of Fourier Series
1.2 Summability of Fourier Series
1.3 A Quick Introduction to Summability Methods
1.4 Key Properties of Summability Kernels
1.5 Pointwise Convergence for Fourier Series
1.6 Norm Convergence of Partial Sums and the Hilbert Transform
2 The Fourier Transform
2.1 Basic Properties of the Fourier Transform
2.2 Invariance and Symmetry Properties of the Fourier Transform
2.3 Convolution and Fourier Inversion
2.4 The Uncertainty Principle
3 Multiple Fourier Series
3.1 Various Methods of Partial Summation
3.2 Examples of Different Types of Summation
3.3 Fourier Multipliers and the Summation of Series
3.4 Applications of the Fourier Multiplier Theorems to Summation of Multiple Trigonometric Series
3.5 The Multiplier Problem for the Ball
4 Spherical Harmonics
4.1 A New Look at Fourier Analysis in the Plane
4.2 Further Results on Spherical Harmonics
5 Fractional Integrals, Singular Integrals, and Hardy Spaces
5.1 Fractional Integrals and Other Elementary Operators
5.2 Prolegomena to Singular Integral Theory
5.3 An Aside on Integral Operators
5.4 A Look at Hardy Spaces in the Complex Plane
5.5 The Real-Variable Theory of Hardy Spaces
5.6 The Maximal-Function Characterization of Hardy Spaces
5.7 The Atomic Theory of Hardy Spaces
5.8 Ode to BMO
6 Modern Theories of Integral Operators
6.1 Spaces of Homogeneous Type
6.2 Integral Operators on a Space of Homogeneous Type
6.3 A New Look at Hardy Spaces
6.4 The T(1) Theorem
7 Wavelets
7.1 Localization in the Time and Space Variables
7.2 Building a Custom Fourier Analysis
7.3 The Haar Basis
7.4 Some Illustrative Examples
7.5 Construction of a Wavelet Basis
8 A Retrospective
8.1 Fourier Analysis: An Historical Overview
Appendices and Ancillary Material
Appendix Ⅰ, The Existence of Testing Functions and Their Density in LP
Appendix Ⅱ, Schwartz Functions and the Fourier Transform
Appendix Ⅲ, The Interpolation Theorems of Marcinkiewicz and Riesz-Thorin
Appendix IV, Hausdorff Measure and Surface Measure
Appendix Ⅴ, Greens Theorem
Appendix Ⅵ, The Banach-Alaoglu Theorem
Appendix Ⅶ, Expressing an Integral in Terms of the Distribution Function
Appendix Ⅷ, The Stone-Weierstrass Theorem
Appendix Ⅸ, Landaus O and o Notation
Table of Notation
Bibiography
Index
内容摘要
本书介绍了调和分析，从其早的开端到的研究进展。遵循历史和概念的起源，本书讨论了单变量和多变量的傅里叶级数、傅里叶变换、球面调和函数、分数次积分、欧氏空间上的奇异积分。从齐性空间的角度来考虑早期观点是本书的精彩之处。书末讨论了小波，它是调和分析中的思想之一。
本书适合研究生、高年级本科生、数学家和任何想快速纵览调和分析的人阅读，读者所需的背景知识包括微积分、集合论、积分理论、序列和级数理论。
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