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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 Integration by parts operator ： ウィキペディア英語版 Integration by parts operator In mathematics, an integration by parts operator is a linear operator used to formulate integration by parts formulae; the most interesting examples of integration by parts operators occur in infinite-dimensional settings and find uses in stochastic analysis and its applications. ==Definition== Let ''E'' be a Banach space such that both ''E'' and its continuous dual space ''E''∗ are separable spaces; let ''μ'' be a Borel measure on ''E''. Let ''S'' be any (fixed) subset of the class of functions defined on ''E''. A linear operator ''A'' : ''S'' → ''L''2(''E'', ''μ''; R) is said to be an integration by parts operator for ''μ'' if :$\backslash int\_\; \backslash mathrm\; \backslash varphi(x)\; h(x)\; \backslash ,\; \backslash mathrm\; \backslash mu(x)\; =\; \backslash int\_\; \backslash varphi(x)\; (A\; h)(x)\; \backslash ,\; \backslash mathrm\; \backslash mu(x)$ for every ''C''1 function ''φ'' : ''E'' → R and all ''h'' ∈ ''S'' for which either side of the above equality makes sense. In the above, D''φ''(''x'') denotes the Fréchet derivative of ''φ'' at ''x''. 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「Integration by parts operator」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.