On Ore rings, linear operators and factorization
type: Item
instance of: scholarly article
title: On Ore rings, linear operators and factorization
zbMATH Open document ID: 0828.16035
author: Manuel Bronstein
author: Marko Petkovšek
published in: Programming and Computer Software
publication date: 1995-08-01T00:00:00Z
review text: Factorization algorithms for linear differential and difference operators from the same point of view are given using Ore polynomials. First Ore polynomials are defined and described by their basic properties. Then these polynomials are considered as linear operators acting on some vector space. This permits to consider the differential and difference operators as particular types of Ore polynomials. Conditions under which factors of degree 1 exist for the corresponding operator are obtained. These conditions correspond to the existence of some special type of solutions of the operators which in some cases of linear differential and difference operators coincide with the rational logarithmic derivatives or hypergeometric solutions. The factors of higher degree were investigated also. The methods used in this work can be applied to the \(q\)-difference operators and convolution type operators.
Mathematics Subject Classification ID: 16U20
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 16Z05
Mathematics Subject Classification ID: 12D05
zbMATH DE Number: 780328
zbMATH Keywords: factorization algorithms
zbMATH Keywords: difference operators
zbMATH Keywords: Ore polynomials
zbMATH Keywords: linear operators
zbMATH Keywords: logarithmic derivatives
zbMATH Keywords: \(q\)-difference operators
zbMATH Keywords: convolution type operators
reviewed by: A. I. Kashu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 780328