Distribution of zero subsequences for Bernstein space and criteria of completeness for exponential system on a segment

Abstract

For $\sigma\in (0,+\infty)$, denote by $B_\sigma^{\infty}$ the Bernstein space (of type $\sigma$) of all entire functions of exponential type $\leq \sigma$ bounded on real axis $\R$. Let $I_d\subset \R$ be a segment of length $d>0$. We announce complete description of non-uniqueness sequences of points for $B_\sigma^\infty$ and criteria of completeness of exponential system in $C(I_d)$ or $L^p(I_d)$ to within one or two exponential functions.