Optimal complexity recovery of band- and energy-limited signals II

AbstractThis paper deals with the recovery of band- and energy-limited signals in Lp(I)-norm from Hermitian information gathered on a given finite interval I. Let mp(ε) be the minimal number of the information pieces required to find an ϵ-accurate approximation to any such signal. We shall prove that limϵ→0+ mp(ϵ)log log 1ϵlog1ϵ = 1 for any p in [1, ∞], and that for sufficiently small ε > 0, Hermitian interpolation using mp(ε)(1 + o(1)) arbitrary nodes yields an ε-approximation in Lp(I)-norm with almost minimal cost