Institute of Mathematics and Informatics Bulgarian Academy of Sciences
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
