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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 Radó–Kneser–Choquet theorem ： ウィキペディア英語版 Radó–Kneser–Choquet theorem In mathematics, the Radó–Kneser–Choquet theorem, named after Tibor Radó, Hellmuth Kneser and Gustave Choquet, states that the Poisson integral of a homeomorphism of the unit circle is a harmonic diffeomorphism of the open unit disk. The result was stated as a problem by Radó and solved shortly afterwards by Kneser in 1926. Choquet, unaware of the work of Radó and Kneser, rediscovered the result with a different proof in 1945. Choquet also generalized the result to the Poisson integral of a homeomorphism from the unit circle to a simple Jordan curve bounding a convex region. ==Statement== Let ''f'' be an orientation-preserving homeomorphism of the unit circle |''z''| = 1 in C and define the Poisson integral of ''f'' by :$\backslash displaystyle\; \backslash int\_0^\; f(\backslash varphi)\backslash cdot\; \backslash ,d\backslash varphi,\}$ for ''r'' < 1. Standard properties of the Poisson integral show that ''F''''f'' is a harmonic function on |''z''| < 1 which extends by continuity to ''f'' on |''z''| = 1. With the additional assumption that ''f'' is orientation-preserving homeomorphism of this circle, ''F''''f'' is an orientation preserving diffeomorphism of the open unit disk. 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「Radó–Kneser–Choquet 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.