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Title: Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory
Authors: Dryanov, Dimiter
Keywords: Paley-Wiener-Schwartz Space
Shannon Sampling Theorem
Tschakaloff-Bernstein Representation Formulas
Levin Transcendental Interpolating Theory
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 33, No 4, (2007), 411p-432p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.
ISSN: 1310-6600
Appears in Collections:Volume 33, Number 4

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