This article is cited in 1 paper

Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition

S. A. Avdonin^ab, S. A. Ivanov<sup>c

a</sup> University of Alaska Fairbanks
^b Moscow Center for Fundamental and Applied Mathematics
^c St. Petersburg Branch of the Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences

Abstract: B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin's result to a more general class of entire functions $F(z)$ with zeros in a strip $\sup|{\operatorname{Im}\lambda_n}|<\infty$ such that $|F(x)|^2$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that $\log|F(x)|$ belongs to the BMO class.

Keywords: Helson–Szegő condition, upper uniform density, exponential Riesz bases.

UDC: 517.547.7

Received: 14.03.2022
Revised: 28.06.2022

DOI: 10.4213/mzm13493

 English version: Mathematical Notes, 2023, 113:2, 165–171

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