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The Clifford-Fourier Transform

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Abstract

A pair of Clifford-Fourier transforms is defined in the framework of Clifford analysis, as operator exponentials with a Clifford algebra-valued kernel. It is a genuine Clifford analysis construct, which is shown to be a refinement of the classical multi-dimensional Fourier transform. An adequate operational calculus is developed.

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Authors and Affiliations

  1. Clifford Research Group, Department of Mathematical Analysis Faculty of Engineering, Ghent University, Galglaan 2, 9000 Gent, Belgium

    Fred Brackx, Nele De Schepper & Frank Sommen

Authors
  1. Fred Brackx
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  2. Nele De Schepper
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  3. Frank Sommen
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Correspondence to Fred Brackx, Nele De Schepper or Frank Sommen.

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Brackx, F., De Schepper, N. & Sommen, F. The Clifford-Fourier Transform. J Fourier Anal Appl 11, 669–681 (2005). https://doi.org/10.1007/s00041-005-4079-9

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  • DOI: https://doi.org/10.1007/s00041-005-4079-9

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