Generating orthogonal matrix polynomials satisfying second order differential equations from a trio of triangular matrices
The method developed in [A.J. Durán, F.A. Grünbaum, Orthogonal matrix polynomials satisfying second order differential equations, Int. Math. Res. Not. 10 (2004) 461–484] led us to consider matrix polynomials that are orthogonal with respect to weight matrices of the form , , and , with satisfying ,...
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/182514 |
| Acesso em linha: | https://hdl.handle.net/11441/182514 https://doi.org/10.1016/j.jat.2008.08.003 |
| Access Level: | acceso abierto |
| Palavra-chave: | Orthogonal matrix polynomials Second order differential equations |
| Resumo: | The method developed in [A.J. Durán, F.A. Grünbaum, Orthogonal matrix polynomials satisfying second order differential equations, Int. Math. Res. Not. 10 (2004) 461–484] led us to consider matrix polynomials that are orthogonal with respect to weight matrices of the form , , and , with satisfying , , , , and , , respectively. Here and are in general two non-commuting matrices. We are interested in sequences of orthogonal polynomials which also satisfy a second order differential equation with differential coefficients that are matrix polynomials , and (independent of ) of degrees not bigger than 2, 1 and 0 respectively. To proceed further and find situations where these second order differential equations hold, we only dealt with the case when one of the matrices or vanishes. The purpose of this paper is to show a method which allows us to deal with the case when , and are simultaneously triangularizable (but without making any commutativity assumption). |
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