%0 Journal Article
%T Matrix differential equations and scalar polynomials satisfying higher order recursions
%A Antonio J. Duran
%A F. Alberto Grščnbaum
%J Mathematics
%D 2008
%I arXiv
%X We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same property. The construction of the correspond- ing family of matrix valued polynomials has been studied in [D1, D2, DV] but the existence of a differential operator having them as common eigen- functions had not been considered This correspondence goes only one way and most matrix valued situations do not arise in this fashion. We illustrate this general construction with a few examples. In the case of some families of scalar valued polynomials introduced in [GH] we take a first look at the algebra of all matrix differential operators that share these common eigenfunctions and uncover a number of phenomena that are new to the matrix valued case.
%U http://arxiv.org/abs/0812.4770v1