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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 Brascamp–Lieb inequality ： ウィキペディア英語版 Brascamp–Lieb inequality In mathematics, the Brascamp–Lieb inequality is a result in geometry concerning integrable functions on ''n''-dimensional Euclidean space R''n''. It generalizes the Loomis–Whitney inequality and Hölder's inequality, and is named after Herm Jan Brascamp and Elliott H. Lieb. The original inequality (called the geometric inequality here) is in .〔H.J. Brascamp and E.H. Lieb, ''Best Constants in Young's Inequality, Its'' ''Converse and Its Generalization to More Than Three Functions'', Adv. in Math. 20, 151–172 (1976).〕 Its generalization, stated first, is in 〔E.H.Lieb, ''Gaussian Kernels have only Gaussian Maximizers'', Inventiones Mathematicae 102, pp. 179–208 (1990).〕 ==Statement of the inequality== Fix natural numbers ''m'' and ''n''. For 1 ≤ ''i'' ≤ ''m'', let ''n''''i'' ∈ N and let ''c''''i'' > 0 so that :$\backslash sum\_^\; c\_\; n\_\; =\; n.$ Choose non-negative, integrable functions :$f\_\; \backslash in\; L^\; \backslash left(\; \backslash mathbb^\; :\; \backslash mathbb^\; \backslash to\; \backslash mathbb^^\}\; \backslash prod\_^\; f\_\; \backslash left(\; B\_\; x\; \backslash right)^\; x\; \backslash leq\; D^\; \backslash prod\_^\; \backslash left(\; \backslash int\_\}\}\; f\_\; (y)\; \backslash ,\; \backslash mathrm\; y\; \backslash right)^^\; c\_\; B\_^\; A\_\; B\_\; \backslash right)\}\; (\; \backslash det\; A\_\; )^\; \backslash right|\; A\_\; \backslash mbox\; n\_\; \backslash times\; n\_\; \backslash mbox\; \backslash right\backslash \}.$ Another way to state this is that the constant ''D'' is what one would obtain by restricting attention to the case in which each $f\_$ is a centered Gaussian function, namely $f\_(y)\; =\; \backslash exp\; \backslash .$ 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「Brascamp–Lieb inequality」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.