Complex versus real orthogonal polynomials of two variables

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.

Keywords:

• complex orthogonal polynomials
• orthogonal polynomials of two variables
• several variables
• complex Hermite
• disk polynomials

Mathematics Subject Classification:

• 33C45
• 33C50

Funding

The work was supported in part by NSF Grant [DMS-1106113].