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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 Dunkl operator ： ウィキペディア英語版 Dunkl operator In mathematics, particularly the study of Lie groups, a Dunkl operator is a certain kind of mathematical operator, involving differential operators but also reflections in an underlying space. Formally, let ''G'' be a Coxeter group with reduced root system ''R'' and ''k''''v'' a multiplicity function on ''R'' (so ''k''''u'' = ''k''''v'' whenever the reflections σ''u'' and σ''v'' corresponding to the roots ''u'' and ''v'' are conjugate in ''G''). Then, the Dunkl operator is defined by: :$T\_i\; f(x)\; =\; \backslash frac\; f(x)\; +\; \backslash sum\_\; k\_v\; \backslash frac\; v\_i$ where $v\_i$ is the ''i''-th component of ''v'', 1 ≤ ''i'' ≤ ''N'', ''x'' in ''R''''N'', and ''f'' a smooth function on ''R''''N''. Dunkl operators were introduced by . One of Dunkl's major results was that Dunkl operators "commute," that is, they satisfy $T\_i\; (T\_j\; f(x))\; =\; T\_j\; (T\_i\; f(x))$ just as partial derivatives do. Thus Dunkl operators represent a meaningful generalization of partial derivatives. ==References== * 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「Dunkl 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.