Optimal complexity recovery of band- and energy-limited signals

AbstractThis paper deals with the recovery of band- and energy-limited signals from a finite set of their samples taken in a given finite interval. Let m(ϵ) be the minimal number of samples required to get an ϵ- accurate approximation of any such signal. We prove that limϵ→0+m(ϵ)log log1/epsi;log1/ϵ = 1, and, for sufficiently small ϵ > 0, Lagrangian interpolation with m(ϵ)(1 + o(1)) arbitrary nodes yields an ϵ-approximation with almost minimal cost