Orthogonal matrix polynomials whose differences are also orthogonal

JOURNAL OF APPROXIMATION THEORY

卷:179

Article

Duran, Antonio J.¹  Sanchez-Canales, Vanesa¹ 

[1] Univ Seville, Dept Anal Matemat, E-41080 Seville, Spain

关键词: Orthogonal matrix polynomials;    Difference equations;    Difference operators;    Charlier polynomials;    Matrix orthogonality;   

DOI  :  10.1016/j.jat.2013.11.012

来源: Elsevier

【 摘 要 】

We characterize orthogonal matrix polynomials (P-n)(n) whose differences (del Pn+1)(n) On are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn),1 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free