Geometric completeness of distribution spaces
type: Item
instance of: scholarly article
title: Geometric completeness of distribution spaces
zbMATH Open document ID: 1041.35004
DOI: 10.1023/A:1024067827698
author: Shiva Shankar
published in: Acta Applicandae Mathematicae
publication date: 2003-08-21T00:00:00Z
review text: The author considers \(\mathcal A\)--submodules \(\mathcal P\) of \({\mathcal A}^ k\), where \(k\in {\mathbb N}\) and \({\mathcal A}={\mathbb C}[\partial_1,\ldots,\partial_n]\) is the ring of linear partial differential operators with constant complex coefficients, and studies properties of the solution spaces \(\text{ker}_{\mathcal F}({\mathcal P})\) associated with \(\mathcal P\) and \(\mathcal F\), where \(\mathcal F\) is a finitely generated \(\mathcal A\)-module and, in particular, any \(\mathcal A\)-submodule of \({\mathcal D}'\) the space of distributions on \({\mathbb R}^ n\). The author also studies the notion of geometrically completeness for a given \({\mathcal F} \subset {\mathcal D}'\) and proves that if \(\mathcal F\) is \(\mathcal A\)-injective then it is geometrically complete and gives an example proving that the converse is not true.
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 35E20
zbMATH DE Number: 1968884
zbMATH Keywords: complete variety
zbMATH Keywords: flat modules
zbMATH Keywords: injective modules
reviewed by: Francisco J. Castro-Jiménez
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1968884