Sampling in Paley–Wiener spaces associated with fractional integro-differential operators

摘要

This paper employs the theory of Kramer analytic kernels established by Everitt et al. (Results in Math. 34 (1998) 310) to derive sampling expansions. The kernels of the recovered transforms are Mittag-Leffler functions of two parameters. These kernels are solutions of certain classes of fractional integro-differential equations. The technique used here is different from the analytic approach by Djrbashian (Harmonic Analysis and Boundary Value Problems in the Complex Domain, BirkHäuser, Basel, 1993).