| Description |
1 online resource (xiii, 349 pages). |
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data file |
| Physical Medium |
polychrome |
| Series |
De Gruyter studies in mathematics ; 3
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De Gruyter studies in mathematics ; 3.
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| Bibliography |
Includes bibliographical references (pages 325-328) and index. |
| Access |
Use copy Restrictions unspecified MiAaHDL |
| Reproduction |
Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2011. MiAaHDL |
| System Details |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
| Processing Action |
digitized 2011 HathiTrust Digital Library committed to preserve MiAaHDL |
| Contents |
24 Analytic AlgebrasChapter 3 Complex Manifolds and the Elementary Theory of Complex Spaces; 30 Bringing in the Sheaves; 31 Ringed Spaces and Local Models of Complex Spaces; 32 Complex Manifolds and Reduced Complex Spaces; 32A Supplement: Submersions and Immersions; 32B Supplement: Examples of Complex Manifolds; 33 Zeros of Polynomials; 33A Supplement: Resultants and Discriminants; 33B Supplement: Proper Mappings and Equivalence Relations; Chapter 4 Complex Spaces; 41 Coherent Sheaves; 42 The Coherence of nO; 43 Complex Spaces. |
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44 Germs of Complex Spaces and Analytic Algebras 45 Discrete and Finite Holomorphic Mappings; 45A Supplement: Image Sheaves; 45B Supplement: The Analytic Spectrum; 46 The Representation Theorem for Prime Germs; 46A Supplement: Injective Holomorphic Mappings between Manifolds of the Same Dimension; 46B Supplement: Universal Denominators for Prime Germs; 47 Hilbert's Nullstellensatz and Cartan's Coherence Theorem; 48 Dimension Theory; 49 Set of Singular Points and Decomposition into Irreducible Components; 49A Supplement: Fiber Products and Quotients. |
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Chapter 1 Regions of Holomorphy 11 Domains of Convergence of Power Series and Reinhardt Domains; 12 Regions of Holomorphy and Holomorphic Convexit; 12A Supplement: Further Extension Theorems for Holomorphic Functions; 12B Supplement: The Edge-of-the-Wedge Theorem; 13 Plurisubharmonic Functions; 14 Pseudoconvex Domains; Part Two: Function Theory on Analytic Sets; Chapter 2 The Weierstrass Preparation Theorem and its Applications; 21 Power Series Algebras; 22 The Weierstrass Theorems; 23 Algebraic Properties of nO0 and; 23A Supplement: Finite Ring-extensions, Normality. |
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Part Three: Function Theory on Stein SpacesChapter 5 Applications of Theorem B; 50 Introductory Remarks on Cohomology; 50A Supplement: Automorphic Functions; 51 Stein Spaces; 51A Supplement: Countable Topology in Complex Spaces; 52 Theorem B and B-Spaces; 53 The Additive Cousin Problem; 53A Supplement: Meromorphic Functions on Reduced Complex Spaces; 54 The Multiplicative Cousin Problem; 54 A Supplement: The Poincaré Problem; 54B Supplement: Holomorphic Line Bundles; 55 Coherent Analytic Sheaves as Fréchet Sheaves; 56 The Exhaustion Theorem. |
| Summary |
Holomorphic Functions Of Several Variables (De Gruyter Studies In Mathematics). |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Language |
English. |
| Subject |
Holomorphic functions.
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Holomorphic functions. |
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Mathematics.
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Mathematics. |
| Genre/Form |
Electronic books.
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| Added Author |
Barthel, Gottfried.
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Kaup, Burchard, 1940-
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| Other Form: |
Print version: Kaup, Ludger, 1939- Holomorphic functions of several variables. Berlin ; New York : Walter de Gruyter, 1983 (DLC) 83010120 |
| ISBN |
9783110838350 (electronic book) |
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3110838354 (electronic book) |
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3110041502 |
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9783110041507 |
| Standard No. |
10.1515/9783110838350 |
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