Ideal intersections in rings of partial differential operators
type: Item
instance of: scholarly article
title: Ideal intersections in rings of partial differential operators
zbMATH Open document ID: 1228.35091
author: Fritz Schwarz
published in: Advances in Applied Mathematics
publication date: 2011-06-14T00:00:00Z
review text: The factorization of linear ordinary differential operators and the corresponding Loewy decomposition is one of the most important tools in solving linear ordinary differential equations in closed form. For linear partial differential operators a corresponding theory is essentially missing, and the present paper is a first step to overcome this deficiency. The author aims at a complete understanding of the left intersection ideals in the respective ring of differential operators and how to obtain a proper analog to the completely reducible components of Loewy. The left intersection ideals for first-order operators in two or three variables over the coefficient ring of rational functions are studied in detail. Also, a complete list of possible types of intersection and sum ideals is given including the corresponding ideals of constraints in the coefficient ring. As expected, the number of possible types is highly increasing with the number of variables. Several figures are provided which are helpful for understanding the branching into the respective cases.
reviewed by: Michael Langenbruch
Mathematics Subject Classification ID: 35G05
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 16S32
zbMATH DE Number: 5907658
zbMATH Keywords: factorization
zbMATH Keywords: Loewy decomposition
zbMATH Keywords: left intersection ideals
describes a project that uses: ALLTYPES
MaRDI profile type: Publication
full work available at URL: j.aam.2010.04.006
OpenAlex ID: W2024834193
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DOI: 10.1016/J.AAM.2010.04.006
description: scientific article; zbMATH DE number 5907658