On a class of non-uniform average sampling expansions and partial reconstruction in subspaces of L 2(ℝ)

Let φ be a function in the Wiener amalgam space W∞(L1) with a non-vanishing property in a neighborhood of the origin for its Fourier transform φ̂, τ = {τn}n∈Z be a sampling set on R and V τ φ be a closed subspace of L2(R) containing all linear combinations of τ -translates of φ. In this paper we prove that every function f ∈ V τ φ is uniquely determined by and stably reconstructed from the sample set Lφ(f) = {∫ R f(t)φ(t− τn)dt } n∈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 φ we provide an estimate to the corresponding error.