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Iwanami Series in Modern Mathematics
Analysis of Several Complex Variables
Takeo Ohsawa, Nagoya University, Japan
cover
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Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
2002; 121 pp; softcover
Volume: 211
ISBN-10: 0-8218-2098-2
ISBN-13: 978-0-8218-2098-8
List Price: US$35
Member Price: US$28
Order Code: MMONO/211
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One of the approaches to the study of functions of several complex variables is to use methods originating in real analysis. In this concise book, the author gives a lucid presentation of how these methods produce a variety of global existence theorems in the theory of functions (based on the characterization of holomorphic functions as weak solutions of the Cauchy-Riemann equations).

Emphasis is on recent results, including an \(L^2\) extension theorem for holomorphic functions, that have brought a deeper understanding of pseudoconvexity and plurisubharmonic functions. Based on Oka's theorems and his schema for the grouping of problems, the book covers topics at the intersection of the theory of analytic functions of several variables and mathematical analysis.

It is assumed that the reader has a basic knowledge of complex analysis at the undergraduate level. The book would make a fine supplementary text for a graduate-level course on complex analysis.

Readership

Graduate students and research mathematicians interested in several complex variables and analytic spaces.

Reviews

"The goal of this admirable little book is ... to ascend rapidly to a few well-chosen peaks."

-- Mathematical Reviews

"Concise booklet ... The author gives a lucid presentation ... The book would make a fine supplementary text for a graduate-level course on complex analysis."

-- Zentralblatt MATH

Table of Contents

  • Holomorphic functions
  • Rings of holomorphic functions and \(\overline{\partial}\) cohomology
  • Pseudoconvexity and plurisubharmonic functions
  • \(L^2\) estimates and existence theorems
  • Solutions of the extension and division problems
  • Bergman kernels
  • Bibliography
  • Index
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