Polya sequences, Toeplitz kernels and gap theorems

Abstract

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.

13 pages

References in corpus (2)

• Beurling-Malliavin theory for Toeplitz kernels
• Spectral gaps for sets and measures

Cited by in corpus (1)

• Spectral gaps for sets and measures