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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 C0-semigroup ： ウィキペディア英語版 C0-semigroup In mathematics, a ''C''0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly continuous semigroups provide solutions of linear constant coefficient ordinary differential equations in Banach spaces. Such differential equations in Banach spaces arise from e.g. delay differential equations and partial differential equations. Formally, a strongly continuous semigroup is a representation of the semigroup (R+,+) on some Banach space ''X'' that is continuous in the strong operator topology. Thus, strictly speaking, a strongly continuous semigroup is not a semigroup, but rather a continuous representation of a very particular semigroup. == Formal definition == A strongly continuous semigroup on a Banach space $X$ is a map $T\; :\; \backslash mathbb\_+\; \backslash to\; L(X)$ such that # $T(0)\; =\; I$,   (identity operator on $X$) # $\backslash forall\; t,s\; \backslash ge\; 0\; :\; \backslash \; T(t\; +\; s)\; =\; T(t)\; T(s)$ # $\backslash forall\; x\_0\; \backslash in\; X:\; \backslash \; \backslash |T(t)\; x\_0\; -\; x\_0\backslash |\; \backslash to\; 0$, as $t\backslash downarrow\; 0$. The first two axioms are algebraic, and state that $T$ is a representation of the semigroup ($\backslash mathbb\_+,+$); the last is topological, and states that the map $T$ is continuous in the strong operator topology. 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「C0-semigroup」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.