The kernel of the generalized Clifford-Fourier transform and its generating function

TL;DR

This paper investigates the generalized Clifford-Fourier transform, providing explicit kernel expressions, polynomial bounds, and a generating function using Laplace transform techniques, especially in even dimensions.

Contribution

It offers explicit kernel formulas, polynomial bounds, and a generating function for the generalized Clifford-Fourier transform, advancing understanding of its structure and properties.

Findings

Explicit kernel expressions in even dimensions

Polynomial bounds for kernel functions

A new generating function for the transform

Abstract

In this paper, we study the generalized Clifford-Fourier transform introduced in [6] using the Laplace transform technique. We give explicit expressions in the even dimensional case, we obtain polynomial bounds for the kernel functions and establish a generating function.