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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 Wiener–Lévy theorem ： ウィキペディア英語版 Wiener–Lévy theorem Wiener–Lévy theorem is a theorem in Fourier analysis, which states that a function of an absolutely convergent Fourier series has an absolutely convergent Fourier series under some conditions. The theorem was named after Norbert Wiener and Paul Lévy. Norbert Wiener first proved Wiener's 1/''f'' theorem, see Wiener's theorem. It states that if has absolutely convergent Fourier series and is never zero, then its inverse also has an absolutely convergent Fourier series. ==Wiener–Levy theorem== Paul Levy generalized Wiener's result, showing that Let $F(\backslash theta\; )\; =\; \backslash sum\backslash limits\_^\backslash infty\; \}\; ,\backslash theta\; \backslash in\; ()$ be a absolutely convergent Fourier series with :. The values of $F(\backslash theta\; )$ lie on a curve $C$, and $H(t)$ is an analytic (not necessarily single-valued) function of a complex variable which is regular at every point of $C$. Then $H())$ has an absolutely convergent Fourier series. The proof can be found in the Zygmund's classic trigonometric series book. 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「Wiener–Lévy theorem」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.