Prolate shift frames and their duals

We investigate frames for the Paley-Wiener space PW_Ω of square-integrable functions bandlimited to [-Ω/2, Ω/2] generated by translates φ_n (t - αℓ) of prolate spheroidal wave-functions ψ_n (where α > 0 and ℓ is an integer). We estimate frame bounds and give a Fourier construction of the dual frames. An ℓ² estimate on the decay of uniform samples of prolate functions is given to show that the computation of the duals can be done efficiently.