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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 Summability kernel ： ウィキペディア英語版 Summability kernel In mathematics, a summability kernel is a family or sequence of periodic integrable functions satisfying a certain set of properties, listed below. Certain kernels, such as the Fejér kernel, are particularly useful in Fourier analysis. Summability kernels are related to approximation of the identity; definitions of an approximation of identity vary,〔http://math.stackexchange.com/questions/114028/approximation-of-the-identity-and-hardy-littlewood-maximal-function〕 but sometimes the definition of an approximation of the identity is taken to be the same as for a summability kernel. ==Definition== Let $\backslash mathbb:=\backslash mathbb/\backslash mathbb$. A summability kernel is a sequence $(k\_n)$ in $L^1(\backslash mathbb)$ that satisfies # $\backslash int\_\backslash mathbbk\_n(t)\backslash ,dt=1$ # $\backslash int\_\backslash mathbb|k\_n(t)|\backslash ,dt\backslash le\; M$ (uniformly bounded) # $\backslash int\_\}|k\_n(t)|\backslash ,dt\backslash to0$ as $n\backslash to\backslash infty$, for every $\backslash delta>0$. Note that if $k\_n\backslash ge0$ for all $n$, i.e. $(k\_n)$ is a positive summability kernel, then the second requirement follows automatically from the first. If instead we take the convention $\backslash mathbb=\backslash mathbb/2\backslash pi\backslash mathbb$, the first equation becomes $\backslash frac\backslash int\_\backslash mathbbk\_n(t)\backslash ,dt=1$, and the upper limit of integration on the third equation should be extended to $\backslash pi$. We can also consider $\backslash mathbb$ rather than $\backslash mathbb$; then we integrate (1) and (2) over $\backslash mathbb$, and (3) over $|t|>\backslash delta$. 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「Summability kernel」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.