Lax-type pairs in the theory of bivariate orthogonal polynomials

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 analyze a Lax-type pair system for the coefficients of the three term relations....

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Bibliographic Details
Published in:Linear algebra and its applications 2024-03
Main Authors: Branquinho, Amílcar, Foulquié-Moreno, Ana, Pérez, Teresa E., Piñar, Miguel A.
Format: Article
Language:English
Subjects:
2D Toda lattice
Block Lax pairs
Two variable orthogonal polynomials
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Summary: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 analyze 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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2024.03.020