Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

Aleksei Kulikov; Alexander Ulanovskii; Ilya Zlotnikov

doi:10.1016/j.aim.2023.109016

paper

Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

arXiv:2210.00504 · doi:10.1016/j.aim.2023.109016

Abstract

Let $Γ$ be a subset of ${0, 1, 2, ...}$ . We show that if $Γ$ has `gaps' then the completeness and frame properties of the system ${t^{k} e^{2 π in t} : n \in Z, k \in Γ}$ differ from those of the classical exponential systems. This phenomenon is closely connected with the existence of certain uniqueness sets for lacunary polynomials.

16 pages, 1 figure