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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 Constructive function theory ： ウィキペディア英語版 Constructive function theory In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximation theory. The term was coined by Sergei Bernstein. ==Example== Let ''f'' be a 2''π''-periodic function. Then ''f'' is ''α''-Hölder for some 0 < ''α'' < 1 if and only if for every natural ''n'' there exists a trigonometric polynomial ''Pn'' of degree ''n'' such that : $\backslash max\_\; |\; f(x)\; -\; P\_n(x)\; |\; \backslash leq\; \backslash frac,$ where ''C''(''f'') is a positive number depending on ''f''. The "only if" is due to Dunham Jackson, see Jackson's inequality; the "if" part is due to Sergei Bernstein, see Bernstein's theorem (approximation theory). 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「Constructive function theory」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.