Quadratic Decomposition of Bivariate Orthogonal Polynomials

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...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2023-06, Vol.20 (3), Article 118
Main Authors: Branquinho, Amílcar, Foulquié-Moreno, Ana, Pérez, Teresa E.
Format: Article
Language:English
Subjects:
Bivariate analysis
Decomposition
Mathematics
Mathematics and Statistics
Polynomials
Weighting functions
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Summary: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 Bäcklund 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.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-023-02307-3