Multiple Orthogonal Polynomials of two real variables

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.

References in corpus (5)

• The nearest neighbor recurrence coefficients for multiple orthogonal polynomials
• Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
• What is $\dots$ a multiple orthogonal polynomial?
• Orthogonal and multiple orthogonal polynomials, random matrices, and Painlevé equations
• Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials