翻訳と辞書 Words near each other ・ Furukawa, Miyagi ・ Furukawabashi Station ・ Furukimi Station ・ Furukuchi Station ・ Furulia ・ Furulund ・ Furulund (station) ・ Furulund, Partille ・ Furulunds IK ・ Furuma Station ・ Furumachi (Niigata) ・ Fursenko ・ Furslide ・ Furst Gabriel or Last Days of the Pirita Monastery ・ Furst Menschikoff ・ Furstenberg boundary ・ Furstenberg's proof of the infinitude of primes ・ Furstenberg's rosette ・ Furstenfeld ・ Fursuit ・ Fursultiamine ・ Fursy Teyssier ・ Furt ・ Furta ・ Furtado ・ Furtadoa ・ Furtados Music ・ Furtei ・ Furth ・ Furth an der Triesting 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 Furstenberg boundary ： ウィキペディア英語版 Furstenberg boundary In potential theory, a discipline within applied mathematics, the Furstenberg boundary is a notion of boundary associated with a group. It is named for Harry Furstenberg, who introduced it in a series of papers beginning in 1963 (in the case of semisimple Lie groups). The Furstenberg boundary, roughly speaking, is a universal moduli space for the Poisson integral, expressing a harmonic function on a group in terms of its boundary values. ==Motivation== A model for the Furstenberg boundary is the hyperbolic disc $D=\backslash$. The classical Poisson formula for a bounded harmonic function on the disc has the form :$f(z)\; =\; \backslash frac\backslash int\_0^\; \backslash hat(e^)\; P(z,e^)\backslash ,\; d\backslash theta$ where ''m'' is the Haar measure on the boundary and ''P'' is the Poisson kernel. Any function ''f'' on the disc determines a function on the group of Möbius transformations of the disc by setting . Then the Poisson formula has the form : $F(g)\; =\; \backslash int\_\backslash hat(gz)\; \backslash ,\; dm(z).$ This function is then harmonic in the sense that it satisfies the mean-value property with respect to a measure on the Möbius group induced from the usual Lebesgue measure of the disc, suitably normalized. The association of a bounded harmonic function to an (essentially) bounded function on the boundary is one-to-one. 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「Furstenberg boundary」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.