翻訳と辞書 Words near each other ・ Enerflex ・ ENERGA anti-tank rifle grenade ・ Energa Gedania Gdańsk ・ Energa Sopot Match Race ・ Energa Toruń ・ Energen ・ Energen Resources Corporation ・ Energen Wave Power ・ Energetic (disambiguation) ・ Energetic (song) ・ Energetic Disassembly ・ Energetic Gamma Ray Experiment Telescope ・ Energetic material ・ Energetic Materials Research and Testing Center ・ Energetic neutral atom ・ Energetic space ・ Energetically Autonomous Tactical Robot ・ Energetically modified cement ・ Energeticism ・ Energetický a průmyslový holding ・ Energetics ・ Energetik ・ Energetik Dushanbe ・ Energetik FK ・ Energetik Əli-Bayramlı FK ・ Energex ・ Energex Rescue Helicopter ・ Energhetic Dubăsari ・ Energi 1 ・ Energia 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 Energetic space ： ウィキペディア英語版 Energetic space In mathematics, more precisely in functional analysis, an energetic space is, intuitively, a subspace of a given real Hilbert space equipped with a new "energetic" inner product. The motivation for the name comes from physics, as in many physical problems the energy of a system can be expressed in terms of the energetic inner product. An example of this will be given later in the article. ==Energetic space== Formally, consider a real Hilbert space $X$ with the inner product $(\backslash cdot|\backslash cdot)$ and the norm $\backslash |\backslash cdot\backslash |$. Let $Y$ be a linear subspace of $X$ and $B:Y\backslash to\; X$ be a strongly monotone symmetric linear operator, that is, a linear operator satisfying * $(Bu|v)=(u|Bv)\backslash ,$ for all $u,\; v$ in $Y$ * $(Bu|u)\; \backslash ge\; c\backslash |u\backslash |^2$ for some constant $c>0$ and all $u$ in $Y.$ The energetic inner product is defined as :$(u|v)\_E\; =(Bu|v)\backslash ,$ for all $u,v$ in $Y$ and the energetic norm is :$\backslash |u\backslash |\_E=(u|u)^\backslash frac\_E\; \backslash ,$ for all $u$ in $Y.$ The set $Y$ together with the energetic inner product is a pre-Hilbert space. The energetic space $X\_E$ is defined as the completion of $Y$ in the energetic norm. $X\_E$ can be considered a subset of the original Hilbert space $X,$ since any Cauchy sequence in the energetic norm is also Cauchy in the norm of $X$ (this follows from the strong monotonicity property of $B$). The energetic inner product is extended from $Y$ to $X\_E$ by : $(u|v)\_E\; =\; \backslash lim\_\; (u\_n|v\_n)\_E$ where $(u\_n)$ and $(v\_n)$ are sequences in ''Y'' that converge to points in $X\_E$ in the energetic norm. 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「Energetic space」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.