泛函分析.pdf

泛函分析.pdf
 

书籍描述

编辑推荐
《泛函分析(英文版)》可供高等院校学专业高年级学生和研究生以及教师参考使用。

作者简介
作者:(美国)斯坦恩(Elias M.Stein) (美国)Rami Shakarchi

目录
Foreword
Preface
Chapter 1.Lp Spaces and Banach Spaces
1 Lp spaces
1.1 The HSlder and Minkowski inequalities
1.2 Completeness of Lp
1.3 Further remarks
2 The case
3 Banach spaces
3.1 Examples
3.2 Linear functionals and the dual of a Banach space
4 The dual space of Lp when
5 More about linear functionals
5.1 Separation of convex sets
5.2 The Hahn-Banach Theorem
5.3 Some consequences
5.4 The problem of measure
6 Complex Lp and Banach spaces
7 Appendix:The dual of C(X)
7.1 The case of positive linear functionals
7.2 The main result
7.3 An extension
8 Exercises
9 Problems
Chapter 2.Lp Spaces in Harmonic Analysis
1 Early Motivations
2 The Riesz interpolation theorem
2.1 Some examples
3 The Lp theory of the Hilbert transform
3.1 The L2 formalism
3.2 The Lp theorem
3.3 Proof of Theorem 3.2
4 The maximal function and weak-type estimates
4.1 The Lp inequality
5 The Hardy space
5.1 Atomic decomposition of H1
5.2 An alternative definition of H1
5.3 Application to the Hilbert transform
6 The space H1 and maximal functions
6.1 The space BMO
7 Exercises
8 Problems
Chapter 3.Distributions:Generalized Functions
1 Elementary properties
1.1 Definitions
1.2 Operations on distributions
1.3 Supports of distributions
1.4 Tempered distributions
1.5 Fourier transform
1.6 Distributions with point supports
2 Important examples of distributions
2.1 The Hilbert transform and pv
2.2 Homogeneous distributions
2.3 Fundamental solutions
2.4 Fundamental solution to general partial differential
equations with constant coefficients
2.5 Parametrices and regularity for elliptic equations
3 Calder6n-Zygmund distributions and Lp estimates
3.1 Defining properties
3.2 The Lp theory
4 Exercises
5 Problems
Chapter 4.Applications of the Baire Category Theorem
1 The Baire category theorem
1.1 Continuity of the limit of a sequence of continuous
functions
1.2 Continuous functions that are nowhere differentiable
2 The uniform boundedness principle
2.1 Divergence of Fourier series
3 The open mapping theorem
3.1 Decay of Fourier coefficients of L1-functions
4 The closed graph theorem
4.1 Grothendieck's theorem on closed subspaces of Lp
……
Chapter 5.Rudiments of Probability Theory
Chapter 6.An Introduction to Brownian Motion
Chapter 7.A Glimpse into Several Complex Variables
Chapter 8.Oscillatory Integrals in Fourier Analysis
Notes and References
Bibliography
Symbol Glossary
Index

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泛函分析

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泛函分析

内容简介
《泛函分析(英文版)》是泛函数的经典教材,作为Rudin的分析学经典著作之一,《泛函分析(英文版)》秉承了内容精练、结构清晰的特点。第2版新增的内容有Kakutani不动点定理,Lamonosov不变子空间定理以及遍历定理等,另外,还适当增加了一些例子和习题。

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