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.