  A separated sequence $\Lambda$ on the real line is called a Polya sequence if
any entire function of zero exponential type bounded on $\Lambda$ is constant.
In this paper we solve the problem by Polya and Levinson that asks for a
description of Polya sets. We also show that the Polya-Levinson problem is
equivalent to a version of the so-called Beurling gap problem on Fourier
transforms of measures. The solution is obtained via a recently developed
approach based on the use of Toeplitz kernels and de Branges spaces of entire
functions.
