Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach
Classical Analysis and ODEs
2025-02-27 v1
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 extensions of a family of discrete Painlev\'e d-PIV equations. We present some nontrivial examples of matrix orthogonal polynomials of Bessel type.
Cite
@article{arxiv.2502.19326,
title = {Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach},
author = {Amílcar Branquinho and Ana Foulquié-Moreno and Assil Fradi and Manuel Mañas},
journal= {arXiv preprint arXiv:2502.19326},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2209.15372