Abstract
The Clifford-Fourier transform was introduced by Brackx, De Schepper and Sommen who subsequently computed its kernel in dimension d=2. Here we compute the kernel of a fractional version of the transform when d=2 and 4. In doing so we solve appropriate wave-type problems on spheres in two and four dimensions. We also give formulae for the solutions of these problems in all even dimensions and hence a means of computing the fractional Clifford-Fourier kernels in even dimensions.
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Acknowledgements
J.A. Hogan gratefully acknowledges the support of the University of Newcastle’s Centre for Computer Assisted Research in Mathematics and its Applications (CARMA) and the Erwin Schrödinger Institute (Vienna). He is especially grateful for the warm hospitality of the staff of the Institute and the University of Vienna’s Numerical Harmonic Analysis Group during his visit. Thanks Roy. Thanks HG.
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Communicated by Chris Heil.
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Craddock, M.J., Hogan, J.A. The Fractional Clifford-Fourier Kernel. J Fourier Anal Appl 19, 683–711 (2013). https://doi.org/10.1007/s00041-013-9274-5
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DOI: https://doi.org/10.1007/s00041-013-9274-5