多復變數

出版社: 世界圖書出版公司; 第1版 (2009年8月1日)

外文書名: Several Complex Variables

平裝: 207頁

正文語種: 英語

開本: 32

ISBN: 7510005175, 9787510005176

條形碼: 9787510005176

尺寸: 22.2 x 15 x 1 cm

重量: 281 g

作者：(德國)格蘭特

《多復變數》內容簡介：The third chapter presents the Weierstrass formula and the Weierstrasspreparation theorem with applications to the ring of convergent powerseries. It is shown that this ring is a factorization, a Noetherian, and a Henselring. furthermore we indicate how the obtained algebraic theorems can beapplied to the local investigation of analytic sets. One achieves deep resultsin this connection by using sheaf theory, the basic concepts of which arediscussed in the fourth chapter. In Chapter V we introduce complex manifoldsand give several examples. We also examine the different closures of C andthe effects of modifications on complex manifolds.

Chapter Ⅰ Holomorphic Functions

1 Power Series

2 Complex Differentiable Functions

3 The Cauchy Integral

4 Identity Theorems

5 Expansion in Reinhardt Domains

6 Real and Complex Differentiability

7 Holomorphic Mappings

Chapter Ⅱ Domains of Holomorphy

1 The Continuity Theorem

2 Pseudoconvexity

3 Holomorphic Convexity

4 The Thullen Theorem

5 Holomorphically Convex Domains:

6 Examples

7 Riemann Domains over Cn

8 Holomorphic Hulls

Chapter Ⅲ The Weierstrass Preparation Theorem

1 The Algebra of Power Series

2 The Weierstrass Formula

3 Convergent Power Series

4 Prime Factorization

5 Further Consequences (Hensel Rings, Noetherian Rings)

6 Analytic Sets

Chapter Ⅳ Sheaf Theory

1 sheaves of Sets

2 Sheaves with Algebraic Structure

3 Analytic Sheaf Morphisms

4 Coherent Sheaves

Chapter Ⅴ Complex Manifolds

1 Complex Ringed Spaces

2 Function Theory on Complex Manifolds

3 Examples of Complex Manifolds

4 Closures of Cn

Chapter Ⅵ Cohomology Theory

1 Flabby Cohomology

2 The Cech Cohomology

3 Double Complexes

4 The Cohomology Sequence

5 Main Theorem on Stein Manifolds

Chapter Ⅶ Real Methods

1 tangential Vectors

2 Differential Forms on Complex Manifolds

3 Cauchy Integrals

4 Dolbeault's Lemma

5 Fine Sheaves (Theorems of Dolbeault and de Rham)

List of symbols

Bibliography

Index