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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 Hilbert's inequality ： ウィキペディア英語版 Hilbert's inequality In analysis, a branch of mathematics, Hilbert's inequality states that : $$ \left|\sum_\dfrac}}\right|\le\pi\displaystyle\sum_|u_|^2. for any sequence ''u''1,''u''2,... of complex numbers. It was first demonstrated by David Hilbert with the constant 2 instead of ; the sharp constant was found by Issai Schur. It implies that the discrete Hilbert transform is a bounded operator in ''ℓ''2. ==Formulation== Let (''u''''m'') be a sequence of complex numbers. If the sequence is infinite, assume that it is square-summable: : Hilbert's inequality (see ) asserts that : $$ \left|\sum_\dfrac}}\right|\le\pi\displaystyle\sum_|u_|^2. 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「Hilbert's 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.