Analysis of several complex variables
著者
書誌事項
Analysis of several complex variables
（Translations of mathematical monographs, v. 211）（Iwanami series in modern mathematics）
American Mathematical Society, c2002
- タイトル別名
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多変数複素解析
A modern introduction to several complex variables
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注記
Originally published: Tokyo : Iwanami Shoten, 1998
Includes bibliographical references (p. 115-117) and index
内容説明・目次
内容説明
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 L2 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.
目次
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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