TY: JOUR
T1 - Quadratic decomposition of bivariate orthogonal polynomials
A1 - Branquinho, Amílcar
A1 - Foulquié-Moreno, Ana
A1 - Pérez, Teresa E.
N2 - 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.
UR - https://ria.ua.pt/handle/10773/36558
Y1 - 2023
PB - Springer