實(shí)分析與復分析（英文版·原書(shū)第3版·典藏版）簡(jiǎn)介，目錄書(shū)摘
2019-11-13 15:40
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作者：京東
實(shí)分析與復分析（英文版·原書(shū)第3版·典藏版）
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內容簡(jiǎn)介: 《實(shí)分析與復分析（英文版·原書(shū)第3版·典藏版）》是分析領(lǐng)域內的一部經(jīng)典著(zhù)作。毫不夸張地說(shuō)，掌握了該書(shū)，對數學(xué)的理解將會(huì )上一個(gè)新臺階。在第3版中，作者對一些新的課題進(jìn)行了討論，并力求全書(shū)條理清晰。
《實(shí)分析與復分析（英文版·原書(shū)第3版·典藏版）》體例優(yōu)美，實(shí)用性很強，列舉的實(shí)例簡(jiǎn)明精彩。無(wú)論是實(shí)分析部分還是復分析部分，基本上對所有給出的命題都進(jìn)行了論證。另外，書(shū)中還附有大量設計巧妙的習題，通過(guò)這些習題可以真實(shí)地檢測出讀者對課程的理解程度，有的還要求對正文中的原理進(jìn)行論證。
《實(shí)分析與復分析（英文版·原書(shū)第3版·典藏版）》體例優(yōu)美，實(shí)用性很強，列舉的實(shí)例簡(jiǎn)明精彩。無(wú)論是實(shí)分析部分還是復分析部分，基本上對所有給出的命題都進(jìn)行了論證。另外，書(shū)中還附有大量設計巧妙的習題，通過(guò)這些習題可以真實(shí)地檢測出讀者對課程的理解程度，有的還要求對正文中的原理進(jìn)行論證。
作者簡(jiǎn)介:沃爾特·魯?。╓alter Rudin） 1953年于杜克大學(xué)獲得數學(xué)博士學(xué)位。曾先后執教于麻省理工學(xué)院、羅切斯特大學(xué)、威斯康星大學(xué)麥迪遜分校、耶魯大學(xué)等。他的主要研究興趣集中在調和分析和復變函數上。除本書(shū)外，他還著(zhù)有《Functional Analysis》（泛函分析）和《Principles of Mathematical Analysis》（數學(xué)分析原理）等其他名著(zhù)。這些教材已被翻譯成十幾種語(yǔ)言，在世界各地廣泛使用。
目錄: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 Baire's 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
Runge's 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
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
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
Mergelyan's theorem
Exercises
Appendix： Hausdorff's Maximality Theorem
Notes and Comments
Bibliography
List of Special Symbols
Index
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 Baire's 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
Runge's 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
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
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
Mergelyan's theorem
Exercises
Appendix： Hausdorff's Maximality Theorem
Notes and Comments
Bibliography
List of Special Symbols
Index
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