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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 Peetre theorem ： ウィキペディア英語版 Peetre theorem In mathematics, the (linear) Peetre theorem, named after Jaak Peetre, is a result of functional analysis that gives a characterisation of differential operators in terms of their effect on generalized function spaces, and without mentioning differentiation in explicit terms. The Peetre theorem is an example of a finite order theorem in which a function or a functor, defined in a very general way, can in fact be shown to be a polynomial because of some extraneous condition or symmetry imposed upon it. This article treats two forms of the Peetre theorem. The first is the original version which, although quite useful in its own right, is actually too general for most applications. == The original Peetre theorem == Let ''M'' be a smooth manifold and let ''E'' and ''F'' be two vector bundles on ''M''. Let :$\backslash Gamma^\backslash infty\; (E),\backslash \; \backslash hbox\backslash \; \backslash Gamma^\backslash infty\; (F)$ be the spaces of smooth sections of ''E'' and ''F''. An ''operator'' :$D:\backslash Gamma^\backslash infty\; (E)\backslash rightarrow\; \backslash Gamma^\backslash infty(F)$ is a morphism of sheaves which is linear on sections such that the support of ''D'' is non-increasing: ''supp Ds'' ⊆ ''supp s'' for every smooth section ''s'' of ''E''. The original Peetre theorem asserts that, for every point ''p'' in ''M'', there is a neighborhood ''U'' of ''p'' and an integer ''k'' (depending on ''U'') such that ''D'' is a differential operator of order ''k'' over ''U''. This means that ''D'' factors through a linear mapping ''i''''D'' from the ''k''-jet of sections of ''E'' into the space of smooth sections of ''F'': :$D=i\_D\backslash circ\; j^k$ where :$j^k:\backslash Gamma^\backslash infty\; E\backslash rightarrow\; J^kE$ is the ''k''-jet operator and :$i\_D:J^kE\backslash rightarrow\; F$ is a linear mapping of vector bundles. 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「Peetre theorem」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.