Sampling Expansions and Interpolation in Unitarily Translation Invariant Reproducing Kernal Hilbert Spaces
Date
2002
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
Sufficient conditions are established in order that, for a fixed infinite
set of sampling points on the full line, a function satisfies a sampling
theorem on a suitable closed subspace of a unitarily translation
invariant reproducing kernel Hilbert space. A number of examples of
such reproducing kernel Hilbert spaces and the corresponding sampling
expansions are given. Sampling theorems for functions on the
half-line are also established in RKHS using Riesz bases in subspaces
of L 2 ( R
+ ).