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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 Beppo-Levi space ： ウィキペディア英語版 Beppo-Levi space In functional analysis, a branch of mathematics, a Beppo-Levi space, named after Beppo Levi, is a certain space of generalized functions. In the following, is the space of distributions, is the space of tempered distributions in , the differentiation operator with a multi-index, and $\backslash widehat$ is the Fourier transform of . The Beppo-Levi space is :$\backslash dot^\; =\; \backslash left\; \backslash ,$ where denotes the Sobolev semi-norm. An alternative definition is as follows: let such that : and define: :$\backslash begin$ H^s &= \left \(\mathbf^n), \int_ |\xi|^| \widehat (\xi)|^2 \, d\xi < \infty \right \} \\ () X^ &= \left \ v \in H^s \right \} \\ \end Then is the Beppo-Levi space. ==References== * Wendland, Holger (2005), ''Scattered Data Approximation'', Cambridge University Press. * Rémi Arcangéli; María Cruz López de Silanes; Juan José Torrens (2007), "An extension of a bound for functions in Sobolev spaces, with applications to (m,s)-spline interpolation and smoothing" ''Numerische Mathematik'' * Rémi Arcangéli; María Cruz López de Silanes; Juan José Torrens (2009), "Estimates for functions in Sobolev spaces defined on unbounded domains" ''Journal of 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「Beppo-Levi space」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.