Quadratic decomposition of bivariate orthogonal polynomials
Classical Analysis and ODEs
2022-02-22 v1
Abstract
We describe bivariate polynomial sequences orthogonal to a symmetric weight function in terms of several bivariate polynomial sequences orthogonal with respect to Christoffel transformations of the initial weight under a quadratic transformation. We analyze the construction of a symmetric bivariate orthogonal polynomial sequence from a given one, orthogonal to a weight function defined on the positive plane. In this description plays an important role a sort of Backlund type matrix transformations for the involved three term matrix coefficients. We take as a case study relations between symmetric orthogonal polynomials defined on the ball and on the simplex.
Cite
@article{arxiv.2202.09575,
title = {Quadratic decomposition of bivariate orthogonal polynomials},
author = {Amílcar Branquinho and Ana Foulquié Moreno and Teresa E. Pérez},
journal= {arXiv preprint arXiv:2202.09575},
year = {2022}
}