Asymptotics of matrix orthogonal polynomials on the real line
Classical Analysis and ODEs
2026-04-21 v3
Abstract
In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well as asymptotic behavior of recurrence coefficients and norms. The main tools are the Riemann-Hilbert formulation and the Deift-Zhou method of steepest descent, adapted to the matrix case. A central role is played by the matrix Szeg\H{o} function, an object that has independent interest.
Keywords
Cite
@article{arxiv.2508.04908,
title = {Asymptotics of matrix orthogonal polynomials on the real line},
author = {Alfredo Deaño and Pablo Román},
journal= {arXiv preprint arXiv:2508.04908},
year = {2026}
}
Comments
41 pages, 7 figures. Extra material on orthonormal matrix orthogonal polynomials and limit zero distribution added in Section 2 and Section 4