翻訳と辞書 Words near each other ・ Fourier domain mode locking ・ Fourier integral operator ・ Fourier inversion theorem ・ Fourier Island ・ Fourier number ・ Fourier operator ・ Fourier optics ・ Fourier profilometry ・ Fourier ptychography ・ Fourier series ・ Fourier shell correlation ・ Fourier sine and cosine series ・ Fourier transform ・ Fourier transform infrared spectroscopy ・ Fourier transform ion cyclotron resonance ・ Fourier transform on finite groups ・ Fourier transform spectroscopy ・ Fourierism ・ Fourier–Bessel series ・ Fourier–Deligne transform ・ Fourier–Motzkin elimination ・ Fourier–Mukai transform ・ Fouriesburg ・ Fouriesburg Commando ・ Fourilles ・ Fourka ・ Fourka (disambiguation) ・ Fourmagnac ・ Fourmarierite ・ Fourme d'Ambert Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fourier transform on finite groups ： ウィキペディア英語版 Fourier transform on finite groups In mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. ==Definitions== The Fourier transform of a function $f\; :\; G\; \backslash rightarrow\; \backslash mathbb\backslash ,$ at a representation $\backslash varrho\; :\; G\; \backslash rightarrow\; GL(d\_\backslash varrho,\; \backslash mathbb)\backslash ,$ of $G\backslash ,$ is :$$ \widehat(\varrho) = \sum_ f(a) \varrho(a). For each representation $\backslash varrho\backslash ,$ of $G\backslash ,$, $\backslash widehat(\backslash varrho)\backslash ,$ is a $d\_\backslash varrho\; \backslash times\; d\_\backslash varrho\backslash ,$ matrix, where $d\_\backslash varrho\backslash ,$ is the degree of $\backslash varrho\backslash ,$. Let $\backslash varrho\_i\backslash ,$ be a complete set of inequivalent irreducible representations of $G$. Then the matrix entries of the $\backslash varrho\_i$ are mutually orthogonal functions on $G$. Since the dimension of the transform space is equal to $|G|$, it follows that $\backslash sum\_i\; d\_^2=|G|$. The inverse Fourier transform at an element $a\backslash ,$ of $G\backslash ,$ is given by :$$ f(a) = \frac \sum_i d_ \text\left(\varrho_i(a^)\widehat(\varrho_i)\right). 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「Fourier transform on finite groups」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.