An Introduction to Complex Analysis in Several Variables
Introduction to Complex Analysis in Several Variables
2nd Edition
Published on 12. February 1973
780 pages
978-0-444-10523-3 (ISBN)
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An Introduction to Complex Analysis in Several Variables
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Lars Hormander
Introduction to Complex Analysis in Several Variables
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10/1973
2nd Edition
Elsevier
€64.45
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Content
- Front Cover
- An Introduction to Complex Analysis in Several Variables
- Contents
- Preface
- 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
- 2.3. The inhomogeneous Cauchy-Riemann equations in a polydisc
- 2.4. 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
- Chapter V. Stein Manifolds
- Summary
- 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
- Chapter VII. Coherent Analytic Sheaves on Stein Manifolds
- Summary
- 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
