Work

Matrix Bessel biorthogonal polynomials: a Riemann–Hilbert approach

Year: 2026

Type: article

Abstract: We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann–Hilbert problem we derive first and second order differential relations for the matrix orthogonal polynomials and functions of second kind. It is shown that the corresponding matrix recurrence coefficients satisfy a non-Abelian extension of a family of discrete Painlevé d-PIV equations. We present some nontrivial examples of matrix orthogonal polynomials of Bessel type.

Source: Arabian Journal of Mathematics

DOI: 10.1007/s40065-026-00632-5

Authors: Amílcar Branquinho, Ana Foulquié-Moreno, Assil Fradi, Manuel Mañas

Institutions: University of Coimbra, University of Aveiro, University of Sousse, Universidad Complutense de Madrid

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Ministerio de Ciencia, Innovación y Universidades, Fundação para a Ciência e a Tecnologia

Awards: G1105844351, Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Centro de Matemática da Universidade de Coimbra