Matrix valued Laguerre polynomials
Classical Analysis and ODEs
2019-08-26 v1
Abstract
Matrix valued Laguerre polynomials are introduced via a matrix weight function involving several degrees of freedom using the matrix nature. Under suitable conditions on the parameters the matrix weight function satisfies matrix Pearson equations, which allow to introduce shift operators for these polynomials. The shift operators lead to explicit expressions for the structures of these matrix valued Laguerre polynomials, such as a Rodrigues formula, the coefficients in the three-term recurrence, differential operators, and expansion formulas.
Cite
@article{arxiv.1811.06592,
title = {Matrix valued Laguerre polynomials},
author = {Erik Koelink and Pablo Román},
journal= {arXiv preprint arXiv:1811.06592},
year = {2019}
}
Comments
20 pages, to appear in Positivity and Noncommutative Analysis Festschrift in Honour of Ben de Pagter (eds. G. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven and A. Wickstead)