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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 differential operator ： ウィキペディア英語版 differential operator In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science). This article considers mainly linear operators, which are the most common type. However, non-linear differential operators, such as the Schwarzian derivative also exist. ==Definition== Assume that there is a map $A$ from a function space $\backslash mathcal\_1$ to another function space $\backslash mathcal\_2$ and a function $f\; \backslash in\; \backslash mathcal\_2$ so that $f$ is the image of $u\; \backslash in\; \backslash mathcal\_1$ i.e.,　$f=A(u)\backslash \; .$ A differential operator is represented as a linear combination finitely generated by $u$ and its derivatives containing higher degree such as :$P(x,D)=\backslash sum\_a\_\backslash alpha(x)\; D^\backslash alpha\backslash \; ,$ where the set of non-negative integers, $\backslash alpha=(\backslash alpha\_1,\backslash alpha\_2,\backslash cdots,\backslash alpha\_n)$ , is called a multi-index, $|\backslash alpha|=\backslash alpha\_1+\backslash alpha\_2+\backslash cdots+\backslash alpha\_n$ called length, $a\_\backslash alpha(x)$ are functions on some open domain in ''n''-dimensional space and $D^\backslash alpha=D^\; D^\; \backslash cdots\; D^\backslash \; .$ The derivative above is one as functions or, sometimes, distributions or hyperfunctions and $D\_j=-i\backslash frac$ or sometimes, $D\_j=\backslash frac$ . 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「differential 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.