多元复分析导论

《多元复分析导论》是2010年9月来自1日世界图书出版公司出版的图书，作者是(德国)谢德曼(Volker Sc360百科heidemann)。

• 书名 多元复分析导论
• 页数 171页
• 出版社 世界图书出版公司
• 装帧 平装

图来自书信息

　　出版社: 世界图书出版公司; 第1版 (2010年9增还济月1日)

　　外文书名: Introduction to Complex Analysis in Several Va山犯耐些riables

　　平装: 171派页

　　正文语种: 英语

　　开本360百科: 16

　　ISBN: 9787510027277, 7510027276

　　条形码: 9787510027277

　　段均设威刻能依尺寸: 25.6 x 18.2 x 0.2 cm

　　重量: 340 g

作者简介

　　作者:(德国)谢德曼(Volker Scheidemann)

内容简介

　　《多元复分析导论》内容简介:The idea for this book came when 列I was an assistant at the Department of Mathe-matics and Computer Science at the Philipps-Univ来自ersity Marburg, Germany. Sev-eral times I faced the task of supporting lectures and seminars on complex analysisof severa果错l variables 360百科and found out that there are very few books on the subject,compared to 氧右息阳封补比雷the vast a款支树超算烧采你前告mount of li红香terature on function theory of one variable, letalone on real variables or basic algebra. Even fewer bo括括料oks, to my understanding,were written primarily with the student in mind. So it was quite hard to find sup-porting examples and exercises that helped the s则括tudent to become familiar withthe fascinating theory of several complex variables.

目录

　　Preface

　　1 Elementary theory of several complex variable十光通叫念盟找面制式答s

　　1.1 Geometry of Cn

　　1.2 Holomorphic functions in several complex variables

　　似经钟任扬够石座边张教1.2.1 Definition of a holomorphic function

　　1.2.2 Basic properties of holo带怎哥盐机限行morphic fun振以当ctions

　　1.2.3 Partially holomorphic functions and the Cauchy-Riemann differential equations

　　1.3 The Cauchy Integr矛乐通容利际al Formula

　　1.4 O (U) as a topological space

　　1.4.1 Locally convex spac轴志致兰谓容慢有es

　　1.4.2 The compact-open topology On C (U, E打)

　　1.4.3 The Theo台女常刻黑吗歌坏之杂rems of Arzel-Ascoli and Montel

　　1.5 Power series and Taylor series

　　1.5.1 Summ杨命际入架增希到息镇硫able families in Banach spaces

　　1.5帮既激绍果常吃原调永频.2 Power series

　　1.5.3 Reinhardt domains and Laurent expansion

　　2 Continuation on circular and polycircular domains

　　2.1 Holomorphic con最tinuation

　　2.2 Representation-theoretic interpretation of the Laurent series

　　2.3 Hartogs' Kugelsatz, Special case

　　3 Biholomorphic maps

　　3.1 The Inverse Function Theorem and Implicit Functions

　　3.2 The Riemann Mapping Problem

　　3.3 Cartan's Uniqueness Theorem

　　4 Analytic Sets

　　4.1 Elementary properties of analytic sets

　　4.2 The Riemann Removable Singularity Theorems

　　5 Hartogs Kugelsatz

　　5.1 Holomorphic Differential Forms

　　5.1.1 Multilinear forms

　　5.1.2' Complex differential forms

　　5.2 The inhomogenous Cauchy-Riemann Differential Equations

　　5.3 Dolbeaut's Lemma

　　5.4 The Kugelsatz of Hartogs

　　6 Continuation on Tubular Domains

　　6.1 Convex hulls

　　6.2 Holomorphically convex hulls

　　6.3 Bochner's Theorem

　　7 Cartan-Thullen Theory

　　7.1 Holomorphically convex sets

　　7.2 Domains of Holomorphy

　　7.3 The Theorem of Cartan-Thullen

　　7.4 Holomorphically convex Reinhardt domains

　　8 Local Properties of holomorphic functions

　　8.1 Local representation of a holomorphic function

　　8.1.1 Germ of a holomorphic function

　　8.1.2 The algebras of formal and of convergent power series

　　8.2 The Weierstrass Theorems

　　8.2.1 The Weierstrass Division Formula

　　8.2.2 The Weierstrass Preparation Theorem

　　8.3 Algebraic properties of C (z1,..., zn}

　　8.4 Hilbert's Nullstellensatz

　　8.4.1 Germs of a set

　　8.4.2 The radical of an ideal

　　8.4.3 Hilbert's Nullstellensatz for principal ideals

　　Register of Symbols

　　Bibliography

　　Index