- 实分析与复分析(英文版原书第3版典藏版)/华章数学原版精品系列
- - 作者：(美)沃尔特·鲁丁
  - 出版社：机械工业
  - ISBN：9787111619550
  - 出版日期：2019/03/01
  - 页数：416
- 售价：31.6

内容大纲
沃尔特·鲁丁著的《实分析与复分析(英文版原书第3版典藏版)/华章数学原版精品系列》是分析领域内的一部经典著作。毫不夸张地说，掌握了本书，对数学的理解将会上一个新台阶。在第3版中，作者对一些新的课题进行了讨论，并力求全书条理清晰。
本书体例优美，实用性很强，列举的实例简明精彩。无论是实分析部分还是复分析部分，基本上对所有给出的命题都进行了论证。另外，书中还附有大量设计巧妙的习题，通过这些习题可以真实地检测出读者对课程的理解程度，有的还要求对正文中的原理进行论证。
作者介绍
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 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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作者介绍

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