On a class of non-uniform average sampling expansions and partial reconstruction in subspaces of L_2(?)

摘要

Let φ be a function in the Wiener amalgam space W_∞(L_1 with a non-vanishing property in a neighborhood of the origin for its Fourier transform φ?, τ = {τ_n}_(nε?) be a sampling set on ? and V~τ_φ be a closed subspace of L_2(?) containing all linear combinations of τ-translates of φ. In this paper we prove that every function f ε V~τ_φ is uniquely determined by and stably reconstructed from the sample set. 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