A new construction of the Clifford-Fourier kernel
Classical Analysis and ODEs
2015-09-08 v1
Abstract
In this paper, we develop a new method based on the Laplace transform to study the Clifford-Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is obtained. When the dimension is even, the inverse Laplace transform may be computed and we obtain the explicit expression for the kernel as a finite sum of Bessel functions. We equally obtain the plane wave decomposition and find new integral representations for the kernel in all dimensions. Finally we define and compute the formal generating function for the even dimensional kernels.
Keywords
Cite
@article{arxiv.1509.01960,
title = {A new construction of the Clifford-Fourier kernel},
author = {Denis Constales and Hendrik De Bie and Pan Lian},
journal= {arXiv preprint arXiv:1509.01960},
year = {2015}
}
Comments
15 pages