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Matrix differential equations and scalar polynomials satisfying higher order recursions

Opened Access Matrix differential equations and scalar polynomials satisfying higher order recursions

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Autor: Durán Guardeño, Antonio José
Grünbaum, Francisco Alberto
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2009-06-01
Publicado en: Journal of Mathematical Analysis and Applications, 354 (1), 1-11.
Tipo de documento: Artículo
Resumen: We show that any scalar differential operator with a family of polynomials as its common eigenfunctions leads canonically to a matrix differential operator with the same property. The construction of the corresponding family of matrix valued polynomials has been studied in [A. Durán, A generalization of Favard's theorem for polynomials satisfying a recurrence relation, J. Approx. Theory 74 (1993) 83–109; A. Durán, On orthogonal polynomials with respect to a positive definite matrix of measures, Canad. J. Math. 47 (1995) 88–112; A. Durán, W. van Assche, Orthogonal matrix polynomials and higher order recurrence relations, Linear Algebra Appl. 219 (1995) 261–280] but the existence of a differential operator having them as common eigenfunctions 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 in...
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Cita: Durán Guardeño, A.J. y Grünbaum, F.A. (2009). Matrix differential equations and scalar polynomials satisfying higher order recursions. Journal of Mathematical Analysis and Applications, 354 (1), 1-11.
Tamaño: 192.6Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43379

DOI: 10.1016/j.jmaa.2008.12.019

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