Centrosymmetric and reverse matrices in bivariate orthogonal polynomials

We study bivariate orthogonal polynomials associated with an inner product that satisfies a symmetry property such that it is invariant when both variables are interchanged. Under that hypothesis, the structure of the polynomial vectors of the orthogonal polynomial systems is described by using cent...

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Bibliographic Details
Authors: Bracciali, Cleonice F. [UNESP], Costa, Glalco S., Pérez, Teresa E.
Format: article
Status:Published version
Publication Date:2024
Country:Brasil
Institution:Universidade Estadual Paulista (UNESP)
Repository:Repositório Institucional da UNESP
Language:English
OAI Identifier:oai:repositorio.unesp.br:11449/298897
Online Access:http://dx.doi.org/10.1016/j.laa.2024.03.037
https://hdl.handle.net/11449/298897
Access Level:Open access
Keyword:Bivariate orthogonal polynomials
Centrosymmetric matrices
Reflexive orthogonal polynomial systems
Reflexive weight functions
Reverse matrices
Description
Summary:We study bivariate orthogonal polynomials associated with an inner product that satisfies a symmetry property such that it is invariant when both variables are interchanged. Under that hypothesis, the structure of the polynomial vectors of the orthogonal polynomial systems is described by using centrosymmetric matrices. Also, we prove that the coefficient matrices of the three-term relations, one for each variable, are connected by a reverse operation over matrices. Finally, several particular cases and examples are analysed.