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arXiv · 2311.05949

Lax-type pairs in the theory of bivariate orthogonal polynomials

Amílcar Branquinho·Ana Foulquié-Moreno·Teresa E. Pérez·Miguel A. Piñar
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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.

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Amílcar Branquinho, Ana Foulquié-Moreno, Teresa E. Pérez, Miguel A. Piñar. 2023-11-10. Lax-type pairs in the theory of bivariate orthogonal polynomials. https://arxiv.org/abs/2311.05949

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