Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials
Classical Analysis and ODEs
2023-04-13 v2 Mathematical Physics
math.MP
Probability
Abstract
A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are integer. From this orthogonality, we derive several equivalent Riemann-Hilbert problems. The proof is based on the fundamental identity of Lee and Yang, which we establish using a new technique.
Cite
@article{arxiv.2212.06526,
title = {Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials},
author = {Sergey Berezin and Arno B. J. Kuijlaars and Iván Parra},
journal= {arXiv preprint arXiv:2212.06526},
year = {2023}
}