Approximation of discrete functions and size of spectrum

Let Λ ⊂ R be a uniformly discrete sequence and S ⊂ R a compact set. It is proved that if there exists a bounded sequence of functions in the Paley-Wiener space PW_S that approximates δ-functions on Λ with l²-error d, then the measure ofS cannot be less than 2π(1 - d²)D+(Λ). This estimate is sharp for every d. A similar estimate holds true when the normsof the approximating functions have a moderate growth; the corresponding sharp growth restriction is found.