A new construction of the Clifford-Fourier kernel

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 e...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2017-04, Vol.23 (2), p.462-483
Main Authors: Constales, Denis, De Bie, Hendrik, Lian, Pan
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Fourier Analysis
Kernels
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical analysis
Partial Differential Equations
Signal,Image and Speech Processing
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Summary: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.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-016-9476-8