| 書目名稱 | Polynomial Convexity | | 編輯 | Edgar Lee Stout | | 視頻video | http://file.papertrans.cn/752/751338/751338.mp4 | | 概述 | Distinctive and comprehensive approach to the theory of polynomially convex sets.Examples and counterexamples illustrate complex ideas | | 叢書名稱 | Progress in Mathematics | | 圖書封面 |  | | 描述 | This book is devoted to an exposition of the theory of polynomially convex sets.Acompact N subset of C is polynomially convex if it is de?ned by a family, ?nite or in?nite, of polynomial inequalities. These sets play an important role in the theory of functions of several complex variables, especially in questions concerning approximation. On the one hand, the present volume is a study of polynomial convexity per se, on the other, it studies the application of polynomial convexity to other parts of complex analysis, especially to approximation theory and the theory of varieties. N Not every compact subset of C is polynomially convex, but associated with an arbitrary compact set, say X, is its polynomially convex hull, X, which is the intersection of all polynomially convex sets that contain X. Of paramount importance in the study of polynomial convexity is the study of the complementary set X X. The only obvious reason for this set to be nonempty is for it to have some kind of analytic structure, and initially one wonders whether this set always has complex structure in some sense. It is not long before one is disabused of this naive hope; a natural problem then is that of giving | | 出版日期 | Book 2007 | | 關(guān)鍵詞 | Complex analysis; Convexity; Pseudoconvexity; convex hull; functional analysis; polynomial convexity; poly | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-8176-4538-0 | | isbn_ebook | 978-0-8176-4538-0Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Birkh?user Boston 2007 |
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