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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 Analytic capacity ： ウィキペディア英語版 Analytic capacity In complex analysis, the analytic capacity of a compact subset ''K'' of the complex plane is a number that denotes "how big" a bounded analytic function from C \ ''K'' can become. Roughly speaking, γ(''K'') measures the size of the unit ball of the space of bounded analytic functions outside ''K''. It was first introduced by Ahlfors in the 1940s while studying the removability of singularities of bounded analytic functions. ==Definition== Let ''K'' ⊂ C be compact. Then its analytic capacity is defined to be :$\backslash gamma(K)\; =\; \backslash sup\; \backslash \backslash setminus\; K),\backslash \; \backslash |f\backslash |\_\backslash infty\backslash leq\; 1,\backslash \; f(\backslash infty)=0\backslash \}$ Here, $\backslash mathcal^\backslash infty\; (U)$ denotes the set of bounded analytic functions ''U'' → C, whenever ''U'' is an open subset of the complex plane. Further, :$f\text{'}(\backslash infty):=\; \backslash lim\_z\backslash left(f(z)-f(\backslash infty)\backslash right)$ :$f(\backslash infty):=\; \backslash lim\_f(z)$ (note that usually $f\text{'}(\backslash infty)\backslash neq\; \backslash lim\_\; f\text{'}(z)$) 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「Analytic capacity」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.