Complex versus real orthogonal polynomials of two variables

2013/07/30 by Xu, Yuan
#33C45 #33C50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.7819

Abstract

Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples.

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• Orthogonal polynomials through the invariant theory of binary forms
• Orthogonal polynomials of several variables
• Multiple Orthogonal Polynomials of two real variables
• Three term relations for a class of bivariate orthogonal polynomials
• Characterization of classical orthogonal polynomials in two variables