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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 Borel–Carathéodory theorem ： ウィキペディア英語版 Borel–Carathéodory theorem In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodory. == Statement of the theorem == Let a function $f$ be analytic on a closed disc of radius ''R'' centered at the origin. Suppose that ''r'' < ''R''. Then, we have the following inequality: :$\backslash |f\backslash |\_r\; \backslash le\; \backslash frac\; \backslash sup\_\; \backslash operatorname\; f(z)\; +\; \backslash frac\; |f(0)|.$ Here, the norm on the left-hand side denotes the maximum value of ''f'' in the closed disc: :$\backslash |f\backslash |\_r\; =\; \backslash max\_\; |f(z)|\; =\; \backslash max\_\; |f(z)|$ (where the last equality is due to the maximum modulus principle). 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「Borel–Carathéodory theorem」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.