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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Holomorphically convex hull ： ウィキペディア英語版 Holomorphically convex hull In mathematics, more precisely in complex analysis, the holomorphically convex hull of a given compact set in the ''n''-dimensional complex space C''n'' is defined as follows. Let $G\; \backslash subset\; \}(G)$ stand for the set of holomorphic functions on $G.$ For a compact set $K\; \backslash subset\; G$, the holomorphically convex hull of $K$ is :$\backslash hat\_G\; :=\; \backslash \; f\; \backslash in\; .$ (One obtains a narrower concept of polynomially convex hull by requiring in the above definition that ''f'' be a polynomial.) The domain $G$ is called holomorphically convex if for every $K\; \backslash subset\; G$ compact in $G$, $\backslash hat\_G$ is also compact in $G$. Sometimes this is just abbreviated as ''holomorph-convex''. When $n=1$, any domain $G$ is holomorphically convex since then $\backslash hat\_G$ is the union of $K$ with the relatively compact components of $G\; \backslash setminus\; K\; \backslash subset\; G$. Also, being holomorphically convex is the same as being a domain of holomorphy (The Cartan–Thullen theorem). These concepts are more important in the case ''n'' > 1 of several complex variables. ==See also== * Stein manifold * Pseudoconvexity 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Holomorphically convex hull」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.