Bispectrality for Matrix Laguerre-Sobolev polynomials
Classical Analysis and ODEs
2023-02-17 v1
Abstract
In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transformation of the corresponding matrix we deduce the connection with a sequence of orthogonal polynomials associated with a Christoffel perturbation of the measure involved in the standard part of the Sobolev inner product. A connection with matrix orthogonal polynomials is stated. The Laguerre-Sobolev type case is studied as an illustrative example. Finally, the bispectrality of such matrix orthogonal polynomials is pointed out.
Keywords
Cite
@article{arxiv.2302.08313,
title = {Bispectrality for Matrix Laguerre-Sobolev polynomials},
author = {Francisco Marcellán and Ignacio Zurrián},
journal= {arXiv preprint arXiv:2302.08313},
year = {2023}
}