2009, Olevskii, Alexander, Ulanovskii, Alexander

Let Λ⊂R be a uniformly discrete sequence and S⊂R a compact set. We prove that if there exists a bounded sequence of functions in Paley-Wiener space PWs, which approximates δ-functions on Λ with l2-error d, then measure(S)≥2π(1−d2)D+(Λ). This estimate is sharp for every d. Analogous estimate holds when the norms of approximating functions have a moderate growth, and we find a sharp growth restriction.

2013, Olevskii, Alexander, Ulanovskii, Alexander

We obtain sharp estimates for the sampling constants in Bernstein spaces when the density of the sampling set is near the critical value.