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实分析与复分析(英文版 原书第3版 典藏版)/(美)沃尔特.鲁丁 [美]沃尔特·鲁丁（Walter Rudin） 9787111619550 机械工业出版社
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作者[美]沃尔特·鲁丁（Walter Rudin）
出版社机械工业出版社
ISBN9787111619550
出版时间2019-03
装帧平装
开本16开
定价79元
货号1201852642
上书时间2024-03-08
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作者简介
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。
目录
Preface
Prologue: The Exponential Function
Chapter 1 Abstract Integration
Set-theoretic notations and terminology
The concept of measurability
Simple functions
Elementary properties of measures
Arithmetic in [0, ∞]
Integration of positive functions
Integration of complex functions
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 Borei measures
Lebesgue measure
Continuity properties of measurable functions
Exercises
Chapter 3 LP-Spaces
Convex functions and inequalities
The Lp-spaces
Approximation by continuous functions
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
Consequences of Baires theorem
Fourier series of continuous functions
Fourier coefficients of L1-functions
The Hahn-Banach theorem
An abstract approach to the Poisson integral
Exercises
Chapter 6 Complex Measures
Total variation
Absolute continuity
Consequences 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 transformations
Exercises
Chapter 8 Integration on Product Spaces
Measurability on cartesian products
Product measures
The Fubini theorem
Completion of product measures
Convolutions
Distribution functions
Exercises
Chapter 9 Fourier Transforms
Formal properties
The inversion theorem
The Plancherel theorem
The Banach algebra Lt
Exercises
Chapter 10 Elementary Properties of Holomorphic
Functions
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 Functions
The Cauchy-Riemann equations
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 Phragrnen-Lindelof method
An interpolation theorem
A converse of the maximum modulus theorem
Exercises
Chapter 13 Approximation by Rational Functions
Preparation
Runges theorem
The Mittag-Leffler theorem
Simply connected regions
Exercises
Chapter 14 Conformal Mapping
Preservation of angles
Linear fractional transformations
Normal families
The Riemann mapping theorem
The class y
Continuity at the boundary
Conformal mapping of an annulus
Exercises
Chapter 15 Zeros of Holomorphic Functions
Infinite products
The Weierstrass factorization theorem
An interpolation problem
Jensens formula
Blaschke products
The Miintz-Szasz theorem
Exercises
Chapter 16 Analytic Continuation
Regular points and singular points
Continuation along curves
The monodromy theorem
Construction of a modular function
The Picard theorem
Exercises
Chapter 17 Hp-Spaces
Subharmonic functions
The spaces Hp and N
The theorem of F. and M. Riesz
Factorization theorems
The shift operator
Conjugate functions
Exercises
Chapter 18 Elementary Theory of Banach Algebras
Introduction
The invertible elements
Ideals and homomorphisms
Applications
Exercises
Chapter 19 Holomorphic Fourier Transforms
Introduction
Two theorems of Paley and Wiener
Quasi-analytic classes
The Denjoy-Carleman theorem
Exercises
Chapter 20 Uniform Approximation by Polynomials
Introduction
Some lemmas
Mergelyans theorem
Exercises
Appendix: Hausdorffs Maximality Theorem
Notes and Comments
Bibliography
List of Spe Symbols
Index
内容摘要
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。
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