Matrix differential equations and scalar polynomials satisfying higher order recursions
| dc.creator | Duran, Antonio J. | |
| dc.creator | Grünbaum, F. Alberto | |
| dc.date | 2008-12-27 | |
| dc.date.accessioned | 2026-07-07T12:22:54Z | |
| dc.date.available | 2026-07-07T12:22:54Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0812.4770 | |
| dc.identifier | http://arxiv.org/abs/0812.4770 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213815 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 15A24,16S32, 39A99, 47B36 | |
| dc.title | Matrix differential equations and scalar polynomials satisfying higher order recursions | |
| dc.type | text |