Multiple Orthogonal Polynomials of two real variables

2024/12/12 by Fernández, Lidia, Villegas, Juan Antonio · 1 citation
#33C45 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2412.09523

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-Padé 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.

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• Bivariate multiple orthogonal polynomials of mixed type on the step-line

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