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arXiv · 2202.09575

Quadratic decomposition of bivariate orthogonal polynomials

Amílcar Branquinho·Ana Foulquié Moreno·Teresa E. Pérez
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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.

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Amílcar Branquinho, Ana Foulquié Moreno, Teresa E. Pérez. 2022-02-19. Quadratic decomposition of bivariate orthogonal polynomials. https://arxiv.org/abs/2202.09575

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