Analysis of several complex variables / Takeo Ohsawa ; translated by Shu Gilbert NakamuraType de document : MonographieCollection : Translations of mathematical monographs, 211Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 2002Description : 1 vol. (XVII-121 p.) ; 22 cmISBN : 0821820982.ISSN : 0065-9282.Bibliographie : Bibliogr. p. 115-117. Index.Sujet MSC : 32A10, Holomorphic functions of several complex variables, Holomorphic functions
32B05, Several complex variables and analytic spaces - Local analytic geometry, Analytic algebras and generalizations, preparation theorems
32W05, Differential operators in several variables, ∂¯ and ∂¯-Neumann operators
32U05, Several complex variables and analytic spaces - Pluripotential theory, Plurisubharmonic functions and generalizationsEn-ligne : Zentralblatt | MathSciNet | AMS
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Bibliogr. p. 115-117. Index
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 (source : AMS)