arXiv subjects

Glalco S. Costa

Publications and source records attributed to Glalco S. Costa.

2 recordsLinked to original sources

arXiv2023

Centrosymmetric and reverse matrices in bivariate orthogonal polynomials

We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and reflexive polynomial systems are directly connected in the context of bivariate orthogonal polynomials. Centrosymmetric matrices, reverse matrices and their connections with reflexive orthogonal polynomial systems are presented. Finally, several particular cases and examples are analysed.

math.CA↗

arXiv2022

Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations

We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyze relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials, also a matrix differential-difference equation for the bivariate orthogonal polynomials is deduced. The extension of the Painlevé equation for the coefficients of the three term relations to the bivariate case and a two dimensional version of the Langmuir lattice are obtained.

math.CA↗