Geodesic
Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory
Serdica Mathematical Journal, Tome 33 (2007) no. 4, pp. 411-432

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We characterize Paley-Wiener-Schwartz space of entire functions as a union of three-parametric linear normed subspaces determined by the type of the entire functions, their polynomial asymptotic on the real line, and the index p ≥ 1 of a Sobolev type Lp-summability on the real line with an appropriate weight function. An entire function belonging to a sub-space of the decomposition is exactly recovered by a sampling series, locally uniformly convergent on the complex plane. The sampling formulas obtained extend the Shannon sampling theorem, certain representation formulas due to Bernstein, and a transcendental interpolating theory due to Levin.
Keywords: Paley-Wiener-Schwartz Space, Shannon Sampling Theorem, Tschakaloff-Bernstein Representation Formulas, Levin Transcendental Interpolating Theory 
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Dryanov, Dimiter. Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory. Serdica Mathematical Journal, Tome 33 (2007) no. 4, pp. 411-432. http://geodesic.mathdoc.fr/item/SMJ2_2007_33_4_a2/