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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 Birkhoff–Kellogg invariant-direction theorem ： ウィキペディア英語版 Birkhoff–Kellogg invariant-direction theorem In functional analysis, the Birkhoff–Kellogg invariant-direction theorem, named after G. D. Birkhoff and O. D. Kellogg, is a generalization of the Brouwer fixed-point theorem. The theorem states that: Let ''U'' be a bounded open neighborhood of 0 in an infinite-dimensional normed linear space ''V'', and let ''F'':∂''U'' → ''V'' be a compact map satisfying ||''F''(''x'')|| ≥ α for some α > 0 for all ''x'' in ∂''U''. Then ''F'' has an invariant direction, ''i.e.'', there exist some ''x''o and some ''λ'' > 0 satisfying ''x''o = ''λF''(''x''o). The Birkhoff–Kellogg theorem and its generalizations by Schauder and Leray have applications to partial differential equations. ==References== 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「Birkhoff–Kellogg invariant-direction 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.