The Fractional Clifford-Fourier Kernel

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Journal Article
Journal of Fourier Analysis and Applications, 2013, 19 (4), pp. 683 - 711
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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. © 2013 Springer Science+Business Media New York.
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