Fourier transforms of orthogonal structures on the paraboloid
Classical Analysis and ODEs
2025-09-08 v1
Abstract
The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal structures on the paraboloid such as Laguerre polynomials on the paraboloid and Jacobi polynomials on the paraboloid, and to define two new families of multivariate orthogonal functions by using Parseval's identity. In addition, some contiguous relations for these families of functions are given, and the obtained results are expressed in terms of the continuous Hahn polynomials.
Keywords
Cite
@article{arxiv.2509.04994,
title = {Fourier transforms of orthogonal structures on the paraboloid},
author = {Hasan Özkan Çetin and Rabia Aktaş Karaman},
journal= {arXiv preprint arXiv:2509.04994},
year = {2025}
}