復變導論

復變導論是世界圖書出版公司的書

基本介紹

• 中文名：復變導論 
• 作者：（美）貝萊恩斯坦
• 出版社：世界圖書出版公司
• 出版時間：2012年1月1日
• 頁數：650 頁
• 定價：79 元 
• 開本：24 開
• 裝幀：平裝 
• ISBN：9787510040658 

內容簡介

貝萊恩斯坦編著的《復變導論（英文影印版）》給出了一個全純函式性質的概述。內容全面，囊括了微分形式、同倫理論、同調理論和全純函式的解析性質、非同質的Cauchy-Riemann方程的可解性和子調和函式理論，引入層理論、覆蓋空間和黎曼曲面。為了幫助讀者更好地理解書中的材料，增加了大量不同難度的習題。

目錄

preface

chapter 1 topology of the complex plane and holomorphic functions

1.1. some linear algebra and differential calculus

1.2. differential forms on an open subset fl of c

1.3. partitions of unity

1.4. regular boundaries

1.5. integration of differential forms of degree 2. the stokes formula

1.6. homotopy. fundamental group

1.7. integration of closed i-forms along continuous paths

1.8. index of a loop

1.9. homology

1.10. residues

1.11. holomorphic functions

chapter 2 analytic properties of holomorphic functions

2.1. integral representation formulas

2.2. the frechet space

2.3. holomorphic maps

2.4. isolated singularities and residues

2.5. residues and the computation of definite integrals

2.6. other applications of the residue theorem

2.7. the area theorem

2.8. conformal mappings

chapter 3 the -equation

3.1. runge'stheorem

3.2. mittag-leffier's theorem

3.3. the weierstrass theorem

3.4. an interpolation theorem

3.5. closed ideals in (ω)

3.6. the operator σ acting on distributions

3.7. mergelyan's theorem

3.8. short survey of the theory of distributions. their relation to thetheory of residues

chapter 4 harmonic and subharmonic functions

4.1. introduction

4.2. a remark on the theory of integration

4.3. harmonic functions

4.4. subharmonic functions

4.5. order and type of subharmonic functions in c

4.6. integral representations

4.7. green functions and harmonic measure

4.8. smoothness up to the boundary of biholomorphic mappings

4.9. introduction to potential theory

chapter 5 analytic continuation and singularities

5.1. introduction

5.2. elementary study of singularities and dirichlet series

5.3. a brief study of the functions f and

5.4. covering spaces

5.5. riemann surfaces

5.6. the sheaf of germs of holomorphic functions

5.7. cocycles

5.8. group actions and covering spaces

5.9. galois coverings

5.10 the exact sequence of a galois covering

5.11. universal covering space

5.12. algebraic functions, i

5.13. algebraic functions, ii

5.14. the periods of a differential form

5.15. linear differential equations

5.16. the index of differential operators