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

Serdica Mathematical Journal (2007)

- Volume: 33, Issue: 4, page 411-432
- ISSN: 1310-6600

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topDryanov, 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 -

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