翻訳と辞書 Words near each other ・ Dinhata I (community development block) ・ Dinhata II (community development block) ・ Dinhata subdivision ・ Dinheirosaurus ・ Dinhing Dapita Sadya ・ Dinho Chingunji ・ Dini ・ Dini Beyk ・ Dini Cabinet ・ Dini continuity ・ Dini criterion ・ Dini Daniel ・ Dini derivative ・ Dini Dimakos ・ Dini Petty ・ Dini test ・ Dini Ya Msambwa ・ Dini's Lucky Club ・ Dini's surface ・ Dini's theorem ・ DinI-like protein family ・ Dinia ・ Dinia (moth) ・ Dinia eagrus ・ Dinia mena ・ Dinia subapicalis ・ Dinic ・ Dinic's algorithm ・ Dinichthyloidea ・ Dinichthys 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 Dini test ： ウィキペディア英語版 Dini test In mathematics, the Dini and Dini-Lipschitz tests are highly precise tests that can be used to prove that the Fourier series of a function converges at a given point. These tests are named after Ulisse Dini and Rudolf Lipschitz. == Definition == Let ''f'' be a function on (), let ''t'' be some point and let δ be a positive number. We define the local modulus of continuity at the point ''t'' by :$\backslash left.\backslash right.\backslash omega\_f(\backslash delta;t)=\backslash max\_\; |f(t)-f(t+\backslash varepsilon)|$ Notice that we consider here ''f'' to be a periodic function, e.g. if ''t'' = 0 and ε is negative then we ''define'' ''f''(ε) = ''f''(2π + ε). The global modulus of continuity (or simply the modulus of continuity) is defined by :$\backslash left.\backslash right.\backslash omega\_f(\backslash delta)\; =\; \backslash max\_t\; \backslash omega\_f(\backslash delta;t)$ With these definitions we may state the main results ''Theorem (Dini's test): Assume a function f satisfies at a point t that'' : ''Then the Fourier series of f converges at t to f(t).'' For example, the theorem holds with $\backslash omega\_f=\backslash log^(\backslash delta^)$ but does not hold with $\backslash log^(\backslash delta^)$. ''Theorem (the Dini-Lipschitz test): Assume a function f satisfies'' :$\backslash omega\_f(\backslash delta)=o\backslash left(\backslash log\backslash frac\backslash right)^.$ ''Then the Fourier series of f converges uniformly to f.'' In particular, any function of a Hölder class satisfies the Dini-Lipschitz test. 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「Dini test」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.