Shannon's sampling theorem in a distributional setting

The classical Shannon sampling theorem states that a signal f with Fourier transform F ∈ L(R) having its support contained in (−π, π) can be recovered from the sequence of samples (f(n))n∈Z via f(t) = ∑ n∈Z f(n) sin(π(t− n)) π(t− n) (t ∈ R). In this article we prove a generalization of this result under the assumption that F ∈ E (R) has support contained in (−π, π).