Darboux equivalence for matrix-valued orthogonal polynomials
Classical Analysis and ODEs
2025-12-09 v1
Abstract
In this work, we give some criteria that allow us to decide when two sequences of matrix-valued orthogonal polynomials are related via a Darboux transformation and to build explicitly such transformation. In particular, they allow us to see when and how any given sequence of polynomials is Darboux related to a diagonal matrix of classic orthogonal polynomials. We also explore the notion of Darboux-irreducibility and study some sequences that are not a Darboux transformation of classical orthogonal polynomials.
Cite
@article{arxiv.2407.20994,
title = {Darboux equivalence for matrix-valued orthogonal polynomials},
author = {Ignacio Bono Parisi and Inés Pacharoni and Ignacio Zurrián},
journal= {arXiv preprint arXiv:2407.20994},
year = {2025}
}