多元复分析导论_在线百科全书查询
多元复分析导论
图书信息
出版社: 世界图书出版公司; 第1版 (2010年9月1日)
外文书名: Introduction to Complex Analysis in Several Variables
平装: 171页
正文语种: 英语
开本: 16
ISBN: 9787510027277, 7510027276
条形码: 9787510027277
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 I was an assistant at the Department of Mathe-matics and Computer Science at the Philipps-University Marburg, Germany. Sev-eral times I faced the task of supporting lectures and seminars on complex analysisof several variables and found out that there are very few books on the subject,compared to the vast amount of literature on function theory of one variable, letalone on real variables or basic algebra. Even fewer books, 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 student to become familiar withthe fascinating theory of several complex variables.
目录
Preface
1 Elementary theory of several complex variables
1.1 Geometry of Cn
1.2 Holomorphic functions in several complex variables
1.2.1 Definition of a holomorphic function
1.2.2 Basic properties of holomorphic functions
1.2.3 Partially holomorphic functions and the Cauchy-Riemann differential equations
1.3 The Cauchy Integral Formula
1.4 O （U） as a topological space
1.4.1 Locally convex spaces
1.4.2 The compact-open topology On C （U, E）
1.4.3 The Theorems of Arzel-Ascoli and Montel
1.5 Power series and Taylor series
1.5.1 Summable families in Banach spaces
1.5.2 Power series
1.5.3 Reinhardt domains and Laurent expansion
2 Continuation on circular and polycircular domains
2.1 Holomorphic continuation
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
