Introduction to the Theory of analytic functions of several complex variables / [Translated from the Russian by A.A. Brown, J.M. Danskin, and E. Hewitt].
Idioma: Inglés Lenguaje original: Ruso Series Translations of mathematical monographs: v. 8, etc.Editor: Providence : American Mathematical Society, 1963 (impresión de 1965)Descripción: v. ; 24 cmTítulos uniformes: Teoriia analiticheskikh funktsii mnogikh kompleksnykh peremennykh. Inglés Tema(s): Functions of several complex variablesOtra clasificación: 32.00Chapter I. Fundamental properties of holomorphic functions in a space of n complex variables [17] Functions of n complex variables, their differentiation and integration. Holomorphic functional element [17] Cauchy integral formula for polycylindrical regions. Fundamental properties of a holomorphic functional element [31] Representation of a holomorphic functional element by power series [38] Preparation theorem of Weierstrass. Analytic sets and surfaces [55] Extension of a space. Concept of holomorphic function at the points at infinity of a space [78] Analytic continuation of functions and sets [90] Holomorphic mappings [103] Chapter II. Fundamental properties of holomorphic functions in plane covering regions. Singular points [117] §8. Plane covering regions over the space Pn [117] §9- Holomorphic functions and analytic sets in plane covering regions. Holomorphicity regions and singular points of holomorphic functions [129] §10. Mappings of regions over the space Pn. Interior-branched regions [146] §11. Plane regions convex relative to some class of holomorphic functions [157] §12. Analytic convexity [172] §13. Holomorphy hulls. Regions with automorphisms [192] Chapter III. Complex spaces [203] §14. Complex analytic manifolds. Complex analytic coverings [203] §15. Holomorphic and meromorphic functions on a complex analytic covering. Complex α-spaces of Behnke-Stein [214] § 16. Complex B -spaces of Serre [224] §17. Normal spaces of H. Cartan [235] §18. Holomorphically complete spaces and manifolds [243] §19. Riemann domains [252] Chapter IV. Integral representations [261] §20. The fundamental theorem of Cauchy-Poincare. Theory of residues on a complex manifold [261] §21. Application of the methods of potential theory to the study of holomorphic forms. The integral formula of Bochner-Martinelli [275] §22. The Bergman-Weil integral formula [288] §23. Integral representations in domains of special type [300] Chapter V. Functions meromorphic in the whole space Cn. Entire functions [323] §24. Functions meromorphic in the extended space [323] §25. Cousin’s theorem [327] §26. Characteristics of the growth of an entire function [338] Bibliography [357] Subject index [369]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 32 F961 (Browse shelf) | Available | A-2959 |
Bibliografía: p. 357-367.
Chapter I. Fundamental properties of holomorphic functions in a space of n complex variables [17] --
Functions of n complex variables, their differentiation and integration. Holomorphic functional element [17] --
Cauchy integral formula for polycylindrical regions. Fundamental properties of a holomorphic functional element [31] --
Representation of a holomorphic functional element by power series [38] --
Preparation theorem of Weierstrass. Analytic sets and surfaces [55] --
Extension of a space. Concept of holomorphic function at the points at infinity of a space [78] --
Analytic continuation of functions and sets [90] --
Holomorphic mappings [103] --
Chapter II. Fundamental properties of holomorphic functions in plane covering regions. Singular points [117] --
§8. Plane covering regions over the space Pn [117] --
§9- Holomorphic functions and analytic sets in plane covering regions. Holomorphicity regions and singular points of holomorphic functions [129] --
§10. Mappings of regions over the space Pn. Interior-branched regions [146] --
§11. Plane regions convex relative to some class of holomorphic functions [157] --
§12. Analytic convexity [172] --
§13. Holomorphy hulls. Regions with automorphisms [192] --
Chapter III. Complex spaces [203] --
§14. Complex analytic manifolds. Complex analytic coverings [203] --
§15. Holomorphic and meromorphic functions on a complex analytic covering. Complex α-spaces of Behnke-Stein [214] --
§ 16. Complex B -spaces of Serre [224] --
§17. Normal spaces of H. Cartan [235] --
§18. Holomorphically complete spaces and manifolds [243] --
§19. Riemann domains [252] --
Chapter IV. Integral representations [261] --
§20. The fundamental theorem of Cauchy-Poincare. Theory of residues on a complex manifold [261] --
§21. Application of the methods of potential theory to the study of holomorphic forms. The integral formula of Bochner-Martinelli [275] --
§22. The Bergman-Weil integral formula [288] --
§23. Integral representations in domains of special type [300] --
Chapter V. Functions meromorphic in the whole space Cn. Entire functions [323] --
§24. Functions meromorphic in the extended space [323] --
§25. Cousin’s theorem [327] --
§26. Characteristics of the growth of an entire function [338] --
Bibliography [357] --
Subject index [369] --
MR, 27 #4945
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