Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

Dryanov, Dimiter. "Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory." Serdica Mathematical Journal 33.4 (2007): 411-432. <http://eudml.org/doc/281488>.

@article{Dryanov2007,
abstract = {2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.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.},
author = {Dryanov, Dimiter},
journal = {Serdica Mathematical Journal},
keywords = {Paley-Wiener-Schwartz Space; Shannon Sampling Theorem; Tschakaloff-Bernstein Representation Formulas; Levin Transcendental Interpolating Theory; Paley-Wiener-Schwartz space; Shannon sampling theorem; Tschakaloff-Bernstein representation formulas; Levin transcendental interpolating theory},
language = {eng},
number = {4},
pages = {411-432},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory},
url = {http://eudml.org/doc/281488},
volume = {33},
year = {2007},
}

TY - JOUR
AU - Dryanov, Dimiter
TI - Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory
JO - Serdica Mathematical Journal
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 33
IS - 4
SP - 411
EP - 432
AB - 2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.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.
LA - eng
KW - Paley-Wiener-Schwartz Space; Shannon Sampling Theorem; Tschakaloff-Bernstein Representation Formulas; Levin Transcendental Interpolating Theory; Paley-Wiener-Schwartz space; Shannon sampling theorem; Tschakaloff-Bernstein representation formulas; Levin transcendental interpolating theory
UR - http://eudml.org/doc/281488
ER -