Analysis of Several Complex Variables

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American Mathematical Soc., 2002 - Mathematics - 121 pages
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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.

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Holomorphic Functions
Rings of Holomorphic Functions and Cohomology
Pseudoconvexity and Plurisubharmonic Functions
Lē Estimates and Existence Theorems
Solutions of the Extension and Division Problems
Bergman Kernels

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