The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations

被引：28

作者：

Bonet, Jose ^{[1
]}

Domanski, Pawel ^{[2
,3
]}

机构：

[1] Univ Politecn Valencia, Dept Matemat Aplicada, Inst Matemat Pura & Aplicada, E-46071 Valencia, Spain

[2] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan, Poland

[3] Polish Acad Sci, Inst Math, Poznan Branch, PL-61614 Poznan, Poland

来源：

ADVANCES IN MATHEMATICS | 2008年 / 217卷 / 02期

关键词：

splitting of short exact sequences; space of distributions; space of ultradistributions in the sense of Beurling; functor Proj(1); functor Ext(1); PLS-space; locally convex space; Frechet space; linear partial differential operator; convolution operator; vector-valued equation; solvability; analytic dependence on parameters; smooth dependence on parameter;

D O I：

10.1016/j.aim.2007.07.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

where E is the dual of a Frechet Schwartz space and X, Y are PLS-spaces, like the spaces of distributions or real analytic functions or their subspaces. In particular, we characterize pairs (E, X) as above such that Ext(1) (E, X) = 0 in the category of PLS-spaces and apply this characterization to many natural spaces X and E. In particular, we discover an extension of the (DN)-(Omega) splitting theorem of Vogt and Wagner. These abstract results are applied to parameter dependence of linear partial differential operators and surjectivity of such operators on spaces of vector-valued distributions. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：561 / 585

页数：25

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