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调和分析概览（影印版）

样章
作者：
Steven G. Krantz
定价：
169.00元
ISBN：
978-7-04-057027-4
版面字数：
610.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2022-02-28
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
分析
暂无
  • 前辅文
  • 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 L p
    • 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, Green’s 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, Landau’s O and o Notation
  • Table of Notation
  • Bibliography
  • Index

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