这本《多元复分析导论》由Volker Scheidemann著,全面介绍了多变量复分析,旨在全面清晰地介绍多变复分析,而非包揽尽可能多的相关材料。书中包括了不少相关的数学概念,如泛函分析和代数,以丰富书的内容。书中还集中讲述了一维的情况,例如著名的Hartog的Kugelsatz,Carton-Thullen定理和Bochner定理。
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书名 | 多元复分析导论 |
分类 | 科学技术-自然科学-数学 |
作者 | (德)谢德曼 |
出版社 | 世界图书出版公司 |
下载 | ![]() |
简介 | 编辑推荐 这本《多元复分析导论》由Volker Scheidemann著,全面介绍了多变量复分析,旨在全面清晰地介绍多变复分析,而非包揽尽可能多的相关材料。书中包括了不少相关的数学概念,如泛函分析和代数,以丰富书的内容。书中还集中讲述了一维的情况,例如著名的Hartog的Kugelsatz,Carton-Thullen定理和Bochner定理。 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 Arzela-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 |
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