On a class of non-uniform average sampling expansions and partial reconstruction in subspaces of L2(R)

Let f be a function in the Wiener amalgam space W-infinity(L-1) with a non-vanishing property in a neighborhood of the origin for its Fourier transform (phi) over cap, tau = {tau(n)}(n is an element of Z) be a sampling set on R and V-phi(tau) be a closed subspace of L-2(R) containing all linear combinations of tau-translates of phi. In this paper we prove that every function f is an element of V-phi(tau) f is uniquely determined by and stably reconstructed from the sample set L-phi(tau)(f) = {integral(R) f(t)<(phi(tau - tau(n)))over bar>dt}(n is an element of Z). As our reconstruction formula involves evaluating the inverse of an infinite matrix we consider a partial reconstruction formula suitable for numerical implementation. Under an additional assumption on the decay rate of phi we provide an estimate to the corresponding error.