Sampling series for differentiable functions of polynomial growth

AbstractThe famous Shannon-Whittaker sampling theorem states that if ƒ(t) = ∝−ππe−itu F(u) du, F ϵ L2 [−π, π] then ƒ can be represented by a sampling sum as f(t)=∑n=∘∘f(n)sinπ(t−n)π(t−n)It is shown here that certain functions of polynomial growth can be approximated by a generalized sampling sum and a rate of convergence of the sum to the function is given