Matrix Jacobi Biorthogonal Polynomials via Riemann-Hilbert problem
Classical Analysis and ODEs
2022-10-03 v1
Abstract
We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann-Hilbert problem we can derive first and second order differential relations that these matrix orthogonal polynomials and the second kind functions associated to them verify. For the corresponding matrix recurrence coefficients, non-Abelian extensions of a family of discrete Painlev\'e d-PIV equations are obtained for the three term recurrence relation coefficients.
Cite
@article{arxiv.2209.15372,
title = {Matrix Jacobi Biorthogonal Polynomials via Riemann-Hilbert problem},
author = {Amílcar Branquinho and Ana Foulquié-Moreno and Assil Fradi and Manuel Mañas},
journal= {arXiv preprint arXiv:2209.15372},
year = {2022}
}