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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 Paraproduct ： ウィキペディア英語版 Paraproduct In mathematics, a paraproduct is a non-commutative bilinear operator acting on functions that in some sense is like the product of the two functions it acts on. According to Svante Janson and Jaak Peetre, in an article from 1988,〔Svante Janson and Jaak Peetre, ("Paracommutators-Boundedness and Schatten-Von Neumann Properties" ), ''Transactions of the American Mathematical Society'', Vol. 305, No. 2 (Feb., 1988), pp. 467–504.〕 "the name 'paraproduct' denotes an idea rather than a unique definition; several versions exist and can be used for the same purposes." This said, for a given operator $\backslash Lambda$ to be defined as a paraproduct, it is normally required to satisfy the following properties: * It should "reconstruct the product" in the sense that for any pair of functions, $(f,\; g)$ in its domain, :: $fg\; =\; \backslash Lambda(f,\; g)\; +\; \backslash Lambda(g,\; f).$ * For any appropriate functions, $f$ and $h$ with $h(0)=0$, it is the case that $h(f)\; =\; \backslash Lambda(f,\; h\text{'}(f))$. * It should satisfy some form of the Leibnitz rule. A paraproduct may also be required to satisfy some form of Hölder's inequality. ==Notes== 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「Paraproduct」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.