Fourier transform of the orthogonal polynomials on the unit ball

TL;DR

This paper derives Fourier transforms of multivariate orthogonal polynomials on the unit ball, introduces a new family of orthogonal functions via Parseval's identity, and expresses results using continuous Hahn polynomials.

Contribution

It provides explicit Fourier transforms for multivariate orthogonal polynomials on the unit ball and introduces a new family of orthogonal functions linked to continuous Hahn polynomials.

Findings

Fourier transforms of multivariate orthogonal polynomials are explicitly derived.

A new family of multivariate orthogonal functions is introduced.

Results are expressed in terms of continuous Hahn polynomials.

Abstract

Fourier transform of multivariate orthogonal polynomials on the unit ball are obtained. By using Parseval's identity, a new family of multivariate orthogonal functions are introduced. The results are expressed in terms of the continuous Hahn polynomials.