Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2569

 Title: Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory Authors: Dryanov, Dimiter Keywords: Paley-Wiener-Schwartz SpaceShannon Sampling TheoremTschakaloff-Bernstein Representation FormulasLevin 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. URI: http://hdl.handle.net/10525/2569 ISSN: 1310-6600 Appears in Collections: Volume 33, Number 4

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