Polya sequences, Toeplitz kernels and gap theorems

Details Polya sequences, Toeplitz kernels and gap theorems Polya sequences, Toeplitz kernels and gap theorems

2009-03-26

arxiv.org/abs/0903.4499v3

Mathematics

Complex Variables

13 pages

Scientific paper

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.

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