《多復變數》是2009年世界圖書出版公司出版的圖書，作者是(德國)格蘭特。本文講了weier strass公式和weierstrass準備定理及其在收斂冪級數環上的套用。以及研究了C的不同閉包和修改對複雜流形的影響。
基本介紹
- 書名：多復變數
- 頁數：207頁
- 出版社：世界圖書出版公司
- 裝幀：平裝
圖書信息,作者簡介,內容簡介,目錄,
圖書信息
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
作者簡介
作者：(德國)格蘭特
內容簡介
《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.
目錄
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
