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Complex Analysis in Banach Spaces: Holomorphic Functions and Domains of Holomorphy in Finite and Infinite Dimensions

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Problems arising from the study of holomorphic continuation and holomorphic approximation have been central in the development of complex analysis in finitely many variables, and constitute one of the most promising lines of research in infinite dimensional complex analysis. This book presents a unified view of these topics in both finite and infinite dimensions.

Author(s): Jorge Mujica (Eds.)
Series: North-Holland Mathematics Studies 120
Publisher: Elsevier Science Ltd
Year: 1986

Language: English
Pages: ii-viii, 1-434

Content:
Editor
Page ii

Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

foreword
Pages vii-viii
Jorge Mujica

Chapter I Polynomials
Pages 1-32

Chapter II Holomorphic Mappings
Pages 33-77

Chapter III Domains of Holomorphy
Pages 79-97

Chapter IV Differentiable Mappings
Pages 99-138

Chapter V Differential Forms
Pages 139-176

Chapter VI Polynomially Convex Domains
Pages 177-210

Chapter VII COMMUTATIVE BANACH ALGEBRAS
Pages 211-244

Chapter VIII Plurisubharmonic Functions
Pages 245-286

Chapter IX The ∂ Equation in Pseudoconvex Domains
Pages 287-310

Chapter X The Levi Problem
Pages 311-330

Chapter XI RIEMANN DOMAINS
Pages 331-360

Chapter XII The Levi Problem in Riemann Domains
Pages 361-395

Chapter XIII Envelopes of Holomorphy
Pages 397-420

Birliography
Pages 421-429

Index
Pages 431-434