DOI: 10.1002/mma.10776 ISSN: 0170-4214

Mittag‐Leffler Functions as Eigenfunctions of the Hilbert Transform

Ahmed A. Abdelhakim
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ABSTRACT

Let and , and fix . We show that is an eigenfunction of the Hilbert transform on , provided that . We also prove that is an eigenfunction of the Hilbert transform for any . The corresponding eigenvalues are computed explicitly.

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