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arXiv · 2210.00504

Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

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.

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Aleksei Kulikov, Alexander Ulanovskii, Ilya Zlotnikov. 2022-10-02. Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials. https://doi.org/10.1016/j.aim.2023.109016

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