Orthogonal matrix polynomials whose differences are also orthogonal
We characterize orthogonal matrix polynomials (Pn)n whose differences (∇Pn+1)n are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn)n are orthogonal. We also construct some illustrative examples. In particular, we show that con...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/167140 |
| Acesso em linha: | https://hdl.handle.net/11441/167140 https://doi.org/10.1016/j.jat.2013.11.012 |
| Access Level: | acceso abierto |
| Palavra-chave: | Orthogonal matrix polynomials Difference equations Difference operators Charlier polynomials Matrix orthogonality |
| Resumo: | We characterize orthogonal matrix polynomials (Pn)n whose differences (∇Pn+1)n are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn)n are orthogonal. We also construct some illustrative examples. In particular, we show that contrary to what happens in the scalar case, in the matrix orthogonality the discrete Pearson equation for the weight matrix W is, in general, independent of whether the orthogonal polynomials with respect to W are eigenfunctions of a second order difference operator with polynomial coefficients. ⃝ |
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