Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

Aleksei Kulikov, Alexander Ulanovskii, Ilya Zlotnikov

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 $\{t^k{e}^{2\pi int}:n\in \mathbb{Z},k\in \Gamma \}$ differ fro…