Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

Aleksei Kulikov; Alexander Ulanovskii; Ilya Zlotnikov

doi:10.1016/j.aim.2023.109016

Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

Classical Analysis and ODEs 2023-04-11 v1 Complex Variables Functional Analysis

Authors: Aleksei Kulikov , Alexander Ulanovskii , Ilya Zlotnikov

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Abstract

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

Keywords

exponential systems completeness frame properties lacunary polynomials uniqueness sets gap condition

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@article{arxiv.2210.00504,
  title  = {Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials},
  author = {Aleksei Kulikov and Alexander Ulanovskii and Ilya Zlotnikov},
  journal= {arXiv preprint arXiv:2210.00504},
  year   = {2023}
}

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16 pages, 1 figure

Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

Abstract

Keywords

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