Irregular Sampling on Shift Invariant Spaces

Abstract

Let V(phi) be a shift invariant subspace of L(2)(R) with a Riesz or frame generator phi(t). We take phi(t) suitably so that the regular sampling expansion : f(t) = Sigma(n is an element of Z) f(n)S(t-n) holds on V(phi). We then find conditions on the generator phi(t) and various bounds of the perturbation under which an irregular sampling expansion: f(t) = Sigma(n is an element of Z) f(n + delta(n))S(n)(t) holds on V(phi). Some illustrating examples are also provided.