Orthogonal matrix polynomials whose differences are also orthogonal

Autores: Antonio José Durán Guardeño , Vanesa Sánchez-Canales
Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 179, Nº 1, 2014, págs. 112-127
Idioma: inglés
DOI: 10.1016/j.jat.2013.11.012
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Resumen
- We characterize orthogonal matrix polynomials (Pn)n whose differences (�ÞPn+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.