Multiple Orthogonal Polynomials of two real variables
Classical Analysis and ODEs
2026-01-13 v1 Numerical Analysis
Numerical Analysis
Abstract
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e approximation, random matrix theory or integrable systems. However, this theory has only been studied in the univariate case. We give a generalization of Multiple Orthogonal Polynomials for two variables. Moreover, an extended version of some of the main properties are given. Additionally, some examples are given along the paper.
Cite
@article{arxiv.2412.09523,
title = {Multiple Orthogonal Polynomials of two real variables},
author = {Lidia Fernández and Juan Antonio Villegas},
journal= {arXiv preprint arXiv:2412.09523},
year = {2026}
}