翻訳と辞書 Words near each other ・ Caratasca Lagoon ・ Carataunas ・ Carate ・ Carate Brianza ・ Carate Urio ・ Caratheodory-π solution ・ Carathis ・ Carathis alayorum ・ Carathis australis ・ Carathis byblis ・ Carathis gortynoides ・ Carathis palpalis ・ Carathis septentrionalis ・ Carathéodory conjecture ・ Carathéodory kernel theorem ・ Carathéodory metric ・ Carathéodory's criterion ・ Carathéodory's existence theorem ・ Carathéodory's extension theorem ・ Carathéodory's theorem ・ Carathéodory's theorem (conformal mapping) ・ Carathéodory's theorem (convex hull) ・ Carathéodory–Jacobi–Lie theorem ・ Caratinga ・ CaratLane ・ Caratoola Recreation Park ・ Caratti ・ Caratunk Falls Archeological District ・ Caratunk, Maine ・ Carau Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Carathéodory metric ： ウィキペディア英語版 Carathéodory metric In mathematics, the Carathéodory metric is a metric defined on the open unit ball of a complex Banach space that has many similar properties to the Poincaré metric of hyperbolic geometry. It is named after the Greek mathematician Constantin Carathéodory. ==Definition== Let (''X'', || ||) be a complex Banach space and let ''B'' be the open unit ball in ''X''. Let Δ denote the open unit disc in the complex plane C, thought of as the Poincaré disc model for 2-dimensional real/1-dimensional complex hyperbolic geometry. Let the Poincaré metric ''ρ'' on Δ be given by :$\backslash rho\; (a,\; b)\; =\; \backslash tanh^\; \backslash frac$ (thus fixing the curvature to be −4). Then the Carathéodory metric ''d'' on ''B'' is defined by :$d\; (x,\; y)\; =\; \backslash sup\; \backslash .$ What it means for a function on a Banach space to be holomorphic is defined in the article on Infinite dimensional holomorphy. 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「Carathéodory metric」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.