Lax-type pairs in the theory of bivariate orthogonal polynomials
Classical Analysis and ODEs
2023-11-13 v1
Abstract
Sequences of bivariate orthogonal polynomials written as vector polynomials of increasing size satisfy a couple of three term relations with matrix coefficients. In this work, introducing a time-dependent parameter, we analyse a Lax-type pair system for the coefficients of the three term relations. We also deduce several characterizations relating the Lax-type pair, the shape of the weight, Stieltjes function, moments, a differential equation for the weight, and the bidimensional Toda-type systems.
Keywords
Cite
@article{arxiv.2311.05949,
title = {Lax-type pairs in the theory of bivariate orthogonal polynomials},
author = {Amílcar Branquinho and Ana Foulquié-Moreno and Teresa E. Pérez and Miguel A. Piñar},
journal= {arXiv preprint arXiv:2311.05949},
year = {2023}
}