Sampling expansions and interpolation in unitarily translation invariant reproducing kernel Hilbert spaces
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. Some examples of such reproducing kernel Hilbert spaces are given with the corresponding sampling expansions. Sampling theorems for functions are established using Riesz bases in subspaces of \(L^2(R^+)\).
unitarily translation invariant subspaces
scientific article; zbMATH DE number 1953654