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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 Carleman's inequality ： ウィキペディア英語版 Carleman's inequality Carleman's inequality is an inequality in mathematics, named after Torsten Carleman, who proved it in 1923〔T. Carleman, ''Sur les fonctions quasi-analytiques'', Conférences faites au cinquième congres des mathématiciens Scandinaves, Helsinki (1923), 181-196.〕 and used it to prove the Denjoy–Carleman theorem on quasi-analytic classes. ==Statement== Let ''a''1, ''a''2, ''a''3, ... be a sequence of non-negative real numbers, then :$\backslash sum\_^\backslash infty\; \backslash left(a\_1\; a\_2\; \backslash cdots\; a\_n\backslash right)^\; \backslash le\; e\; \backslash sum\_^\backslash infty\; a\_n.$ The constant ''e'' in the inequality is optimal, that is, the inequality does not always hold if ''e'' is replaced by a smaller number. The inequality is strict (it holds with "<" instead of "≤") if some element in the sequence is non-zero. 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「Carleman'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.