翻訳と辞書 Words near each other ・ Rifaat al-Assad ・ Rifaat Eid ・ Rifaat El-Fanagily ・ Rifaat el-Mahgoub ・ Rifaat Garrana ・ Rifaat Hussain ・ Rifaat Turk ・ Rifabutin ・ Rifaina ・ Rifalazil ・ Rifampicin ・ Riesz mean ・ Riesz potential ・ Riesz rearrangement inequality ・ Riesz representation theorem ・ Riesz sequence ・ Riesz space ・ Riesz theorem ・ Riesz transform ・ Riesz's lemma ・ Riesz–Fischer theorem ・ Riesz–Markov–Kakutani representation theorem ・ Riesz–Thorin theorem ・ Riet ・ Riet River ・ Riet River (Doring) ・ Riet, Germany ・ Rietavas ・ Rietavas Manor ・ Rietavas Municipality 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 Riesz sequence ： ウィキペディア英語版 Riesz sequence In mathematics, a sequence of vectors (''x''''n'') in a Hilbert space $(H,\backslash langle\backslash cdot,\backslash cdot\backslash rangle)$ is called a Riesz sequence if there exist constants :$c\backslash left(\; \backslash sum\_n\; |\; a\_n|^2\; \backslash right)\; \backslash leq\; \backslash left\backslash Vert\; \backslash sum\_n\; a\_n\; x\_n\; \backslash right\backslash Vert^2\; \backslash leq\; C\; \backslash left(\; \backslash sum\_n\; |\; a\_n|^2\; \backslash right)$ for all sequences of scalars (''a''''n'') in the ℓ''p'' space ℓ2. A Riesz sequence is called a Riesz basis if :$\backslash overline\; =\; H$ . ==Theorems== If ''H'' is a finite-dimensional space, then every basis of ''H'' is a Riesz basis. Let $\backslash varphi$ be in the ''L''''p'' space ''L''2(R), let :$\backslash varphi\_n(x)\; =\; \backslash varphi(x-n)$ and let $\backslash hat$ denote the Fourier transform of ''φ''. Define constants ''c'' and ''C'' with :$1.\; \backslash quad\; \backslash forall\; (a\_n)\; \backslash in\; \backslash ell^2,\backslash \; \backslash \; c\backslash left(\; \backslash sum\_n\; |\; a\_n|^2\; \backslash right)\; \backslash leq\; \backslash left\backslash Vert\; \backslash sum\_n\; a\_n\; \backslash varphi\_n\; \backslash right\backslash Vert^2\; \backslash leq\; C\; \backslash left(\; \backslash sum\_n\; |\; a\_n|^2\; \backslash right)$ :$2.\; \backslash quad\; c\backslash leq\backslash sum\_\backslash left|\backslash hat(\backslash omega\; +\; 2\backslash pi\; n)\backslash right|^2\backslash leq\; C$ The first of the above conditions is the definition for (''φ''''n'') to form a Riesz basis for the space it spans. 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「Riesz sequence」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.