Matrix polynomials satisfying first order differential equations and three term recurrence relations

Authors:
Mirta M. Castro
Affiliations:
Universidad de Sevilla, Dpto. Matemática Aplicada II, E.U.P. c. Virgen de África 7, 41011, Sevilla, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 4
Cited 0

Topics in matrix analysis

Topics in matrix analysis
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Abstract

We describe families of matrix valued polynomials satisfying simultaneously a first order differential equation and a three term recurrence relation. Our goal is to address the classification of the matrix valued polynomials satisfying first order differential equations through the solutions of the so-called bispectral problem. At the heart of this lies the need to solve some complicated nonlinear equations with matrix coefficients called ad-conditions. The solutions of these equations are studied under a variety of sufficient conditions on its coefficients.