Summary
Hankel transforms are representations of the conformal inversion operator in Hilbert space. Their action on eigenfunctions of the dilatation operator exists and is consistent, however, only in the sense of analytically regularised integrals. Special cases of this action reduce to Fourier transforms, more specifically to sine and cosine transforms, of these eigenfunctions. These transforms are, in general, not Cauchy-convergent. It is shown here that they may be analytically regularised by Cesàro summability.
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Basili, C., Etim, E. & Pallotta, M. Special cases of the regularisation of the conformal inversion transform by Cesàro summability. Nuov Cim A 103, 1681–1692 (1990). https://doi.org/10.1007/BF02887293
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DOI: https://doi.org/10.1007/BF02887293