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A new construction of the Clifford-Fourier kernel

Denis Constales (UGent) , Hendrik De Bie (UGent) and Pan Lian (UGent)
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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
Clifford-Fourier transform, Laplace transform, Bessel function, Plane wave decomposition

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MLA
Constales, Denis, et al. “A New Construction of the Clifford-Fourier Kernel.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 23, no. 2, SPRINGER BIRKHAUSER, 2017, pp. 462–83, doi:10.1007/s00041-016-9476-8.
APA
Constales, D., De Bie, H., & Lian, P. (2017). A new construction of the Clifford-Fourier kernel. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 23(2), 462–483. https://doi.org/10.1007/s00041-016-9476-8
Chicago author-date
Constales, Denis, Hendrik De Bie, and Pan Lian. 2017. “A New Construction of the Clifford-Fourier Kernel.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 23 (2): 462–83. https://doi.org/10.1007/s00041-016-9476-8.
Chicago author-date (all authors)
Constales, Denis, Hendrik De Bie, and Pan Lian. 2017. “A New Construction of the Clifford-Fourier Kernel.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 23 (2): 462–483. doi:10.1007/s00041-016-9476-8.
Vancouver
1.
Constales D, De Bie H, Lian P. A new construction of the Clifford-Fourier kernel. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. 2017;23(2):462–83.
IEEE
[1]
D. Constales, H. De Bie, and P. Lian, “A new construction of the Clifford-Fourier kernel,” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 23, no. 2, pp. 462–483, 2017.
@article{8530982,
  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.}},
  author       = {{Constales, Denis and De Bie, Hendrik and Lian, Pan}},
  issn         = {{1069-5869}},
  journal      = {{JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS}},
  keywords     = {{Clifford-Fourier transform,Laplace transform,Bessel function,Plane wave decomposition}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{462--483}},
  publisher    = {{SPRINGER BIRKHAUSER}},
  title        = {{A new construction of the Clifford-Fourier kernel}},
  url          = {{http://dx.doi.org/10.1007/s00041-016-9476-8}},
  volume       = {{23}},
  year         = {{2017}},
}

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