Quadratic decomposition of bivariate orthogonal polynomials

• Autor(a) principal: Branquinho, Amílcar
• Data de Publicação: 2023
• Outros Autores: Foulquié-Moreno, Ana, Pérez, Teresa E.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/36558
• topic: Bivariate orthogonal polynomials; Quadratic decomposition process; Backlund-type relations

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.