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- W2950921175 abstract "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." @default.
- W2950921175 created "2019-06-27" @default.
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- W2950921175 date "2008-12-27" @default.
- W2950921175 modified "2023-10-01" @default.
- W2950921175 title "Matrix differential equations and scalar polynomials satisfying higher order recursions" @default.
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