Quadratic Decomposition of Bivariate Orthogonal Polynomials
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Bivariate orthogonal polynomialsQuadratic decomposition processBäcklund-type relations
Branquinho, A., Foulquié-Moreno, A. & Pérez, T.E. Quadratic Decomposition of Bivariate Orthogonal Polynomials. Mediterr. J. Math. 20, 118 (2023). [https://doi.org/10.1007/s00009-023-02307-3]
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 B¨acklund 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.