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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 Gowers norm ： ウィキペディア英語版 Gowers norm In mathematics, in the field of additive combinatorics, a Gowers norm or uniformity norm is a class of norm on functions on a finite group or group-like object which are used in the study of arithmetic progressions in the group. It is named after Timothy Gowers, who introduced it in his work on Szemerédi's theorem. == Definition == Let ''f'' be a complex-valued function on a finite Abelian group ''G'' and let ''J'' denote complex conjugation. The Gowers ''d''-norm is :$\backslash Vert\; f\; \backslash Vert\_^\; =\; \backslash mathbf\_\; \backslash prod\_\; f\backslash left(\backslash right)\; \backslash \; .$ Gowers norms are also defined for complex valued functions ''f'' on a segment ''()='', where ''N'' is a positive integer. In this context, the uniformity norm is given as $\backslash Vert\; f\; \backslash Vert\_\; =\; \backslash Vert\; \backslash tilde\; \backslash Vert\_\backslash mathbb)\}/\backslash Vert\; 1\_\; \backslash Vert\_\backslash mathbb)\}$, where $\backslash tilde\; N$ is a large integer, $1\_$ denotes the indicator function of ''()'', and $\backslash tilde\; f(x)$ is equal to $f(x)$ for $x\; \backslash in\; ()$ and $0$ for all other $x$. This definition does not depend on $\backslash tilde\; N$, as long as $\backslash tilde\; N\; >\; 2^d\; N$. 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「Gowers norm」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.