UID:
almahu_9947367600602882
Format:
1 online resource (227 p.)
Edition:
2nd ed.
ISBN:
9780720424577
,
9780444105233 (e-book)
Series Statement:
North-Holland Mathematical Library ; Volume 7
Content:
An Introduction to Complex Analysis in Several Variables
Note:
Description based upon print version of record.
,
Front Cover; An Introduction to Complex Analysis in Several Variables; Preface; Contents; List of Symbols; Chapter I. Analytic Functions of One Complex Variable; Summary; 1.1. Preliminaries; 1.2. Cauchy's integral formula and its applications; 1.3. The Runge approximation theorem; 1.4. The Mittag-Leffler theorem; 1.5. The Weierstrass theorem; 1.6. Subharmonic functions; Notes; Chapter II. Elementary Properties of Functions of Several Complex Variables; Summary; 2.1. Preliminaries; 2.2. Applications of Cauchy's integral formula in polydiscs
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2.3. The inhomogeneous Cauchy-Riemann equations in a polydisc2.4. Power series and Reinhardt domains; 2.5. Domains of holomorphy; 2.6. Pseudoconvexity and plurisubharmonicity; 2.7. Runge domains; Notes; Chapter III. Applications to Commutative Banach Algebras; Summary; 3.1. Preliminaries; 3.2. Analytic functions of elements in a Banach algebra; Notes; Chapter IV. L2 Estimates and Existence Theorems for the C Operator; Summary; 4.1. Preliminaries; 4.2. Existence theorems in pseudoconvex domains; 4.3. Approximation theorems; 4.4. Existence theorems L2 spaces; 4.5. Analytic functionals; Notes
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Chapter V. Stein ManifoldsSummary; 5.1. Definitions; 5.2. L2 estimates and existence theorems for the c operator; 5.3. Embedding of Stein manifolds; 5.4. Envelopes of holomorphy; 5.5. The Cousin problems on a Stein manifold; 5.6. Existence and approximation theorems for sections of an analytic vector bundle; 5.7. Almost complex manifolds; Notes; Chapter VI. Local Properties of Analytic Functions; Summary; 6.1. The Weierstrass preparation theorem; 6.2. Factorization in the ring A0 of germs of analytic functions; 6.3. Finitely generated A0-modules; 6.4. The Oka theorem; Notes
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Chapter VII. Coherent Analytic Sheaves on Stein ManifoldsSummary; 7.1. Definition of sheaves; 7.2. Existence of global sections of a coherent analytic sheaf; 7.3. Cohomology groups with values in a sheaf; 7.4. The cohomology groups of a Stein manifold with coefficients in a coherent analytic sheaf; 7.5. The de Rham theorem; 7.6. Cohomology with bounds and constant coefficient differential equations; Notes; Bibliography; Index
,
English
Additional Edition:
ISBN 0-7204-2457-7
Additional Edition:
ISBN 0-444-10523-9
Language:
English
