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https://hdl.handle.net/10316/113166
Title: | Quadratic Decomposition of Bivariate Orthogonal Polynomials | Authors: | Branquinho, Amílcar Foulquié Moreno, Ana Pérez, Teresa E. |
Keywords: | Bivariate orthogonal polynomials; quadratic decomposition process; B¨acklund-type relations | Issue Date: | 2023 | Publisher: | Springer Nature | Project: | Open access funding provided by FCT—FCCN (b-on). | Serial title, monograph or event: | Mediterranean Journal of Mathematics | Volume: | 20 | Issue: | 3 | 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 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. | URI: | https://hdl.handle.net/10316/113166 | ISSN: | 1660-5446 1660-5454 |
DOI: | 10.1007/s00009-023-02307-3 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais FCTUC Matemática - Artigos em Revistas Internacionais |
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