English

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.

Keywords

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

R2 v1 2026-06-28T21:58:59.435Z