Sampling Expansions and Interpolation in Unitarily Translation Invariant Reproducing Kernal Hilbert Spaces

2002
Authors
van der Mee, C.V.M.
Nashed, M.Z.
Seatzu, S.
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 + ).