A new construction of the Clifford-Fourier kernel

被引：0
|
作者：
Denis Constales
Hendrik De Bie
Pan Lian
机构：
[1] Faculty of Engineering and Architecture – Ghent University,Department of Mathematical Analysis
[2] Harbin Institute of Technology,Department of Mathematics
来源：
Journal of Fourier Analysis and Applications | 2017年 / 23卷
关键词：
Clifford-Fourier transform; Laplace transform; Bessel function; Plane wave decomposition; 42B10; 30G35; 15A66; 44A10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：462 / 483
页数：21
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