实分析与复分析（英文版·原书第3版·典藏版） mobi 下载 网盘 caj lrf pdf txt 阿里云

本书是分析领域内的一部经典著作。主要内容包括：抽象积分、正博雷尔测度、LP-空间、希尔伯特空间的初等理论、巴拿赫空间技巧的例子、复测度、微分、积空间上的积分、傅里叶变换、全纯函数的初等性质、调和函数、*大模原理、有理函数逼近、共形映射、全纯函数的零点、解析延拓、HP-空间、巴拿赫代数的初等理论、全纯傅里叶变换、用多项式一致逼近等。另外，书中还附有大量设计巧妙的习题。本书体例优美，实用性很强，列举的实例简明精彩，基本上对所有给出的命题都进行了论证，适合作为高等院校数学专业高年级本科生和研究生的教材。

《实分析与复分析（英文版）》目录：

Preface

Prologue: The Exponential Function

Chapter 1 Abstract Integration

Set-theoretic notati*** and terminology

The concept of measurability

Simple functi***

Elementary properties of measures

Arithmetic in [0, ]

Integration of positive functi***

Integration of complex functi***

The role played by sets of measure zero

Exercises

Chapter 2 Positive Borel Measures

Vector spaces

Topological preliminaries

The Riesz representation theorem

Regularity properties of Borel measures

Lebesgue measure

Continuity properties of measurable functi***

Exercises

Chapter 3 LP-Spaces

Convex functi*** and inequalities

The Lp-spaces

Approximation by continuous functi***

Exercises

Chapter 4 Elementary Hilbert Space Theory

Inner products and linear functionals

Orthonormal sets

Trigonometric series

Exercises

Chapter 5 Examples of Banach Space Techniques

Banach spaces

C***equences of Baire's theorem

Fourier series of continuous functi***

Fourier coefficients of L1-functi***

The Hahn-Banach theorem

An abstract approach to the Poisson integral

Exercises

Chapter 6 Complex Measures

Total variation

Absolute continuity

C***equences of the Radon-Nikodym theorem

Bounded linear functionals on Lp

The Riesz representation theorem

Exercises

Chapter 7 Differentiation

Derivatives of measures

The fundamental theorem of Calculus

Differentiable transformati***

Exercises

Chapter 8 Integration on Product Spaces

Measurability on cartesian products

Product measures

The Fubini theorem

Completion of product measures

Convoluti***

Distribution functi***

Exercises

Chapter 9 Fourier Transforms

Formal properties

The inversion theorem

The Plancherel theorem

The Banach algebra L1

Exercises

Chapter 10 Elementary Properties of Holomorphic

Functi***

Complex differentiation

Integration over paths

The local Cauchy theorem

The power series representation

The open mapping theorem

The global Cauchy theorem

The calculus of residues

Exercises

Chapter 11 Harmonic Functi***

The Cauchy-Riemann equati***

The Poisson integral

The mean value property

Boundary behavior of Poisson integrals

Representation theorems

Exercises

Chapter 12 The Maximum Modulus Principle

Introduction

The Schwarz lemma

The Phragmen-Lindelof method

An interpolation theorem

A converse of the maximum modulus theorem

Exercises

Chapter 13 Approximation by Rational Functi***

Preparation

Runge's theorem

The Mittag-Leffler theorem

Simply connected regi***

Exercises

Chapter 14 Conformal Mapping

Preservation of angles

Linear fractional transformati***

Normal families

The Riemann mapping theorem

The class

Continuity at the boundary

Conformai mapping of an annulus

Exercises

Chapter 15 Zeros of Holomorphic Functi***

Infinite products

The Weierstrass factorization theorem

An interpolation problem

Jensen's formula

Blaschke products

The Miintz-Szasz theorem

Exercises

Chapter 16 Analytic Continuation

Regular points and singular points

Continuation along curves

The monodromy theorem

C***truction of a modular function

The Picard theorem

Exercises

Chapter 17 Hp-Spaces

Subharmonic functi***

The spaces Hr and N

The theorem of F. and M. Riesz

Factorization theorems

The shift operator

Conjugate functi***

Exercises

Chapter 18 Elementary Theory of Banach Algebras

Introduction

The invertible elements

Ideals and homomorphisms

Applicati***

Exercises

Chapter 19 Holomorphic Fourier Transforms

Introduction

Two theorems of Paley and Wiener

Quasi-***ytic classes

The Denjoy-Carleman theorem

Exercises

Chapter 20 Uniform Approximation by Polynomials

Introduction

Some iemmas

Mergelyan's theorem

Exercises

Appendix: Hausdorff's Maximality Theorem

Notes and Comments

Bibliography

List of Special Symbols

Index

沃尔特·鲁丁（Walter Rudin） 1953年于杜克大学获得数学博士学位。曾先后执教于麻省理工学院、罗切斯特大学、威斯康星大学麦迪逊分校、耶鲁大学等。他的主要研究兴趣集中在调和分析和复变函数上。除本书外，他还著有《Functional Analysis》（泛函分析）和《Principles of Mathematical Analysis》（数学分析原理）等其他名著。这些教材已被翻译成十几种语言，在世界各地广泛使用。

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书籍介绍

本书是分析领域内的一部经典著作。主要内容包括：抽象积分、正博雷尔测度、LP-空间、希尔伯特空间的初等理论、巴拿赫空间技巧的例子、复测度、微分、积空间上的积分、傅里叶变换、全纯函数的初等性质、调和函数、最大模原理、有理函数逼近、共形映射、全纯函数的零点、解析延拓、HP-空间、巴拿赫代数的初等理论、全纯傅里叶变换、用多项式一致逼近等。另外，书中还附有大量设计巧妙的习题。本书体例优美，实用性很强，列举的实例简明精彩，基本上对所有给出的命题都进行了论证，适合作为高等院校数学专业高年级本科生和研究生的教材。