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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 Bernstein's theorem (approximation theory) ： ウィキペディア英語版 Bernstein's theorem (approximation theory) In approximation theory, Bernstein's theorem is a converse to Jackson's theorem. The first results of this type were proved by Sergei Bernstein in 1912. For approximation by trigonometric polynomials, the result is as follows: Let ''f'': (2π ) → C be a 2''π''-periodic function, and assume ''r'' is a natural number, and 0 < ''α'' < 1. If there exists a number ''C''(''f'') > 0 and a sequence of trigonometric polynomials ''n'' ≥ ''n''0 such that : $\backslash deg\backslash ,\; P\_n\; =\; n~,\; \backslash quad\; \backslash sup\_\; |f(x)\; -\; P\_n(x)|\; \backslash leq\; \backslash frac\{n^\{r\; +\; \backslash alpha\}\}~,$ then ''f'' = ''P''''n''0 + ''φ'', where ''φ'' has a bounded ''r''-th derivative which is α-Hölder continuous. ==See also== * Bernstein's lethargy theorem * Constructive function 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「Bernstein's theorem (approximation 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.