On Ore rings, linear operators and factorization
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.
scientific article; zbMATH DE number 780328