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Title: Quadratic decomposition of bivariate orthogonal polynomials
Author: Branquinho, Amílcar
Foulquié-Moreno, Ana
Pérez, Teresa E.
Keywords: Bivariate orthogonal polynomials
Quadratic decomposition process
Backlund-type relations
Issue Date: 17-Feb-2023
Publisher: Springer
Abstract: We describe the relation between the systems of bivariate orthogonal polynomial associated to a symmetric weight function and associated to some particular Christoffel modifications of the quadratic decomposition of the original weight. We analyze the construction of a symmetric bivariate orthogonal polynomial sequence from a given one, orthogonal to a weight function defined on the first quadrant of the plane. In this description, a sort of Backlund type matrix transformations for the involved three term matrix coefficients plays an important role. Finally, we take as a case study relations between the classical orthogonal polynomials defined on the ball and those on the simplex.
Peer review: yes
DOI: 10.1007/s00009-023-02307-3
ISSN: 1660-5446
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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