Lax-type pairs in the theory of bivariate orthogonal polynomials (Preprint)

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Type: Preprint
National /International: International
Title: Lax-type pairs in the theory of bivariate orthogonal polynomials
Publication Date: 2023-11
Authors: - Amílcar Branquinho
- Ana Foulquié-Moreno
- Teresa E. Pérez
- Miguel A. Piñar
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. 

Institution: arXiv:2311.05949
Online version: https://arxiv.org/abs/2311.05949
Download: Not available
 
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