Polya sequences, Toeplitz kernels and gap theorems

2009/03/26 by Mishko Mitkovski, Mitkovski, Mishko, Alexei Poltoratski +1 · 2 citations
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0903.4499

openalex publication_date 2009/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A separated sequence Λ on the real line is called a Polya sequence if any entire function of zero exponential type bounded on Λ 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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