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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 Homogeneous distribution ： ウィキペディア英語版 Homogeneous distribution :''Not to be confused with uniform distribution'' In mathematics, a homogeneous distribution is a distribution ''S'' on Euclidean space R''n'' or } that is homogeneous in the sense that, roughly speaking, :$S(tx)\; =\; t^m\; S(x)\backslash ,$ for all ''t'' > 0. More precisely, let $\backslash mu\_t\; :\; x\backslash mapsto\; x/t$ be the scalar division operator on R''n''. A distribution ''S'' on R''n'' or } is homogeneous of degree ''m'' provided that :$S()\; =\; t^mS()$ for all positive real ''t'' and all test functions φ. The additional factor of ''t''−''n'' is needed to reproduce the usual notion of homogeneity for locally integrable functions, and comes about from the Jacobian change of variables. The number ''m'' can be real or complex. It can be a non-trivial problem to extend a given homogeneous distribution from R''n'' \ to a distribution on R''n'', although this is necessary for many of the techniques of Fourier analysis, in particular the Fourier transform, to be brought to bear. Such an extension exists in most cases, however, although it may not be unique. ==Properties== If ''S'' is a homogeneous distribution on R''n'' \ of degree α, then the weak first partial derivative of ''S'' :$\backslash frac$ has degree α−1. Furthermore, a version of Euler's homogeneous function theorem holds: a distribution ''S'' is homogeneous of degree α if and only if :$\backslash sum\_^n\; x\_i\backslash frac\; =\; \backslash alpha\; S.$ 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「Homogeneous distribution」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.