书籍详情
复分析（英文版）
作者：Elias M.Stein，Rami Shakarchi 著
出版社：世界图书出版公司
出版时间：2007-01-01
ISBN：9787506282314
定价：¥38.00
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内容简介
本书由在国际上享有盛誉的普林斯顿大学教授Stein等撰写而成， 是一部为数学及相关专业大学二年级和三年级学生编写的教材，理论与实践并重。为了便于非数学专业的学生学习，全书内容简明、易懂，读者只需掌握微积分和线性代数知识。关于本书的详细介绍，请见“影印版前言”。本书已被哈佛大学和加利福尼亚理工学院选为教材。与本书相配套的教材《傅立叶分析导论》和《实分析》也已影印出版。
作者简介
SteIn在国际上享有盛誉，现任美国普林斯顿大学数学系教授。他是当代分析，特别是调和分析领域领袖人物之一。古典调和分析最困难问题之一是推广到多维。他是多维欧氏调和分析的创造者之一，为此他发展了许多先进工具，如奇异积分、Radon变换、极大函数等。他还发展了多个实变元的Hardy空间理论，推广了1971年F J0hn和L.Nirenberg的重要发现：即Hardy空间与BMO空间的对偶。他在群上的调和分析方面也有贡献，例如同R.Kunze一起发现所谓Kunze-stein现象。除此之外，他对多复变问题也做出了突出成绩。除了研究工作之外，他的许多著作成为影响学科发展的重要参考文献。为此，他荣获1984年美国数学会Steele奖。由于他的成就，1974年被选为美国国家科学院院士，1982年被选为美国文理学院院士，1993年获得瑞士科学院颁发的schock奖，1999年获得世界性Wolf数学奖。
目录
Foreword
Introductlon
Chapter 1．Preliminaries to Complex Analysis
l Complex numbers and the eompicx plane
1.1 Basic properties
l.2 Convergence
1.3 Sets in tim complex plane
2 Functions on the complex plane
2.l Conltinuous fnetions
2.2 Holomorphic fimctions
2.3 P0weI series
3 Integration along crvcs
4 Exorcises
Chapter 2 Cauchy’s Theorem and Its Applications
1 Goursat’s theorem
2 Local existencc of primitives and Cauchy s theorem in a
disc
3 EvaIuatlon of some integrals
4 Cauchy’s integral formulas
5 1lrther applications
5.1 Morera’s tImorem
5.2 Sequences of holomorphic functions
5.3 Holomorphic functions defined in terms of integrals
5.4 Schwarz reflection principle
5.5 Runge’s approxlnlatlon theorem
6 Exereises
7 Problems
Chapter 3．Meromorphic Functions and the Logarithm
1 Zeros and polcs
2 The residue formuia
2.l Examples
3 Singularities and meromorphic functions
4 The argmuent principle and applications
5 Homotopies and simply connected domains
6 The complex logarithm
7 Fourier series and harmonic functions
8 Exercises
9 Problenis
Chapter 4. The Fourier Transforin
1 The class
2 Action of the Fourier transform on
3 Palev-wiener tbeorem
4 Exercises
5 Problems
Chapter 5. Entire Functions
1 Jensen's formUla
2 Functions of finite order
3 Infinite products
3.1 Generalities
3.2 Example: the product foemula for the sine function
4 Weierstrass infinite products
5 Hadamard's factorozatoon theorem
6 Exercises
7 Problems
Chapter 6. The Gamma and Zeta Functions
1 The gamma function
1.1 Analytic continuation
1.2 Furtiicr properties of F
2 The zeta function
2.1 Functional equation and analytic continuation
3 Exercises
4 Problems
Chapter 7. The Zeta Function and Prime Number The-orem
1 Zeros of tile zeta function
hl Esthnates for 1/C(S)
2 Reduction to the functions
2.1 Proof of the asymptotics for
Note on interchanging double sums
3 Exercises
4 problems
Chapter 8. Conformal Mappings
Chapter 9. An Introduction to Elliptic Functions
Chapter 10. Applications of Theta Functions
Appendix A: Asymptotics
Appendix B: Simple Connectivity and Jordan Curve Theorem
Notes and References
Bibliography
Symbol Glossary
Index
Introductlon
Chapter 1．Preliminaries to Complex Analysis
l Complex numbers and the eompicx plane
1.1 Basic properties
l.2 Convergence
1.3 Sets in tim complex plane
2 Functions on the complex plane
2.l Conltinuous fnetions
2.2 Holomorphic fimctions
2.3 P0weI series
3 Integration along crvcs
4 Exorcises
Chapter 2 Cauchy’s Theorem and Its Applications
1 Goursat’s theorem
2 Local existencc of primitives and Cauchy s theorem in a
disc
3 EvaIuatlon of some integrals
4 Cauchy’s integral formulas
5 1lrther applications
5.1 Morera’s tImorem
5.2 Sequences of holomorphic functions
5.3 Holomorphic functions defined in terms of integrals
5.4 Schwarz reflection principle
5.5 Runge’s approxlnlatlon theorem
6 Exereises
7 Problems
Chapter 3．Meromorphic Functions and the Logarithm
1 Zeros and polcs
2 The residue formuia
2.l Examples
3 Singularities and meromorphic functions
4 The argmuent principle and applications
5 Homotopies and simply connected domains
6 The complex logarithm
7 Fourier series and harmonic functions
8 Exercises
9 Problenis
Chapter 4. The Fourier Transforin
1 The class
2 Action of the Fourier transform on
3 Palev-wiener tbeorem
4 Exercises
5 Problems
Chapter 5. Entire Functions
1 Jensen's formUla
2 Functions of finite order
3 Infinite products
3.1 Generalities
3.2 Example: the product foemula for the sine function
4 Weierstrass infinite products
5 Hadamard's factorozatoon theorem
6 Exercises
7 Problems
Chapter 6. The Gamma and Zeta Functions
1 The gamma function
1.1 Analytic continuation
1.2 Furtiicr properties of F
2 The zeta function
2.1 Functional equation and analytic continuation
3 Exercises
4 Problems
Chapter 7. The Zeta Function and Prime Number The-orem
1 Zeros of tile zeta function
hl Esthnates for 1/C(S)
2 Reduction to the functions
2.1 Proof of the asymptotics for
Note on interchanging double sums
3 Exercises
4 problems
Chapter 8. Conformal Mappings
Chapter 9. An Introduction to Elliptic Functions
Chapter 10. Applications of Theta Functions
Appendix A: Asymptotics
Appendix B: Simple Connectivity and Jordan Curve Theorem
Notes and References
Bibliography
Symbol Glossary
Index
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