翻訳と辞書 Words near each other ・ Boehm House ・ Boehm syndrome ・ Boehm system ・ Boehm system (clarinet) ・ Boehm's bush squirrel ・ Boehm's gerbil ・ Boehm-Boteler baronets ・ Boehme's giant day gecko ・ Boehmeria ・ Boehmeria australis ・ Boehmeria calophleba ・ Boehmeria cylindrica ・ Boehmeria jamaicensis ・ Boehmeria macrophylla ・ Boehmeria platyphylla ・ Boehmians ・ Boehmite ・ Boehringer ・ Boehringer Ingelheim ・ Boehringer Laboratories ・ Boeil-Bezing ・ Boeill Creek, New South Wales ・ Boeing ・ Boeing 247 ・ Boeing 2707 ・ Boeing 307 Stratoliner ・ Boeing 314 Clipper ・ Boeing 367 ・ Boeing 367-80 ・ Boeing 377 Stratocruiser 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 Boehmians ： ウィキペディア英語版 Boehmians In mathematics, Boehmians are objects obtained by an abstract algebraic construction of "quotients of sequences." The original construction was motivated by regular operators introduced by T. K. Boehme. Regular operators are a subclass of Mikusiński operators, that are defined as equivalence classes of convolution quotients of functions on $[0,\backslash infty\; )$. The original construction of Boehmians gives us a space of generalized functions that includes all regular operators and has the algebraic character of convolution quotients. On the other hand, it includes all distributions eliminating the restriction of regular operators to $[0,\backslash infty\; )$. Since the Boehmians were introduced in 1981, the framework of Boehmians has been used to define a variety of spaces of generalized functions on $\backslash mathbb^N$ and generalized integral transforms on those spaces. It was also applied to function spaces on other domains, like locally compact groups and manifolds. == The general construction of Boehmians == Let $X$ be an arbitrary nonempty set and let $G$ be a commutative semigroup acting on $X$. Let $\backslash Delta$ be a collection of sequences of elements of $G$ such that the following two conditions are satisfied: (1) If $(\backslash phi\_n),\; (\backslash psi\_n)\; \backslash in\; \backslash Delta$, then $(\backslash phi\_n\backslash psi\_n)\; \backslash in\; \backslash Delta$, (2) If $x,y\backslash in\; X$ and $\backslash phi\_n\; x\; =\; \backslash phi\_n\; y$ for some $(\backslash phi\_n)\; \backslash in\; \backslash Delta$ and all $n\backslash in\backslash mathbb$, then $x=y$. Now we define a set of pairs of sequences: $\backslash mathcal\; =\; \backslash \; \backslash \}$. In $\backslash mathcal$ we introduce an equivalence relation: $((x\_n),(\backslash phi\_n))$ ~ $((y\_n),(\backslash psi\_n))$ if $\backslash phi\_m\; y\_n\; =\backslash psi\_n\; x\_m\; \backslash text\; m,\; n\backslash in\; \backslash mathbb$. The space of Boehmians $\backslash mathcal\; (X,\backslash Delta\; )$ is the space of equivalence classes of $\backslash mathcal$, that is $\backslash mathcal\; (X,\backslash Delta\; )=\backslash mathcal/$~. 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「Boehmians」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.