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多元复分析导论PDF|Epub|txt|kindle电子书版本网盘下载

（德）Volker Scheidemann著著
出版社：世界图书出版公司北京公司
ISBN：9787510027277
出版时间：2010
标注页数：172页
文件大小：70MB
文件页数：181页
主题词：多变量－复分析－英文

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图书目录

1 Elementary theory of several complex variables1

1.1 Geometry of Cn1

1.2 Holomorphic functions in several complex variables7

1.2.1 Definition of a holomorphic function7

1.2.2 Basic properties of holomorphic functions10

1.2.3 Partially holomorphic functions and the Canchy-Riemann differential equations13

1.3 The Cauchy Integral Formula17

1.4 O(U)as a topological space19

1.4.1 Locally convex spaces20

1.4.2 The compact-open topology on C(U,E)23

1.4.3 The Theorems of Arzelà-Ascoli and Montel28

1.5 Power series and Taylor series34

1.5.1 Summable families in Banach spaces34

1.5.2 Power series35

1.5.3 Reinhardt domains and Laurent expansion38

2 Continuation on circular and polycircular domains47

2.1 Holomorphic continuation47

2.2 Representation-theoretic interpretation of the Laurent series54

2.3 Hartogs' Kugelsatz,Special case56

3 Biholomorphic maps59

3.1 The Inverse Function Theorem and Implicit Functions59

3.2 The Riemann Mapping Problem64

3.3 Cartan's Uniqueness Theorem67

4 Analytic Sets71

4.1 Elementary properties of analytic sets71

4.2 The Riemann Removable Singularity Theorems75

5 Hartogs' Kugelsatz79

5.1 Holomorphic Differential Forms79

5.1.1 Multilinear forms79

5.1.2 Complex differential forms82

5.2 The inhomogenous Cauchy-Riemann Differential Equations88

5.3 Dolbeaut's Lemma90

5.4 The Kugelsatz of Hartogs94

6 Continuation on Tubular Domain97

6.1 Convex hulls97

6.2 Holomorphically convex hulls100

6.3 Bochner's Theorem106

7 Cartan-Thullen Theory111

7.1 Holomorphically convex sets111

7.2 Domains of Holomorphy115

7.3 The Theorem of Cartan-Thullen118

7.4 Holomorphically convex Reinhardt domains121

8 Local Properties of holomorphic functions125

8.1 Local representation of a holomorphic function125

8.1.1 Germ of a holomorphic function125

8.1.2 The algebras of formal and of convergent power series127

8.2 The Weierstrass Theorems135

8.2.1 The Weierstrass Division Formula138

8.2.2 The Weierstrass Preparation Theorem142

8.3 Algebraic properties of C{z1,...,zn}145

8.4 Hilbert's Nullstellensatz151

8.4.1 Germs of a set152

8.4.2 The radical of an ideal156

8.4.3 Hilbert's Nullstellensatz for principal ideals160

Bibliography167

Index169