Spectral synthesis for exponentials and logarithmic length
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Publication:6352198
DOI10.1007/S11856-022-2341-3zbMath1511.30002arXiv2010.13201MaRDI QIDQ6352198
Aleksei Kulikov, Anton D. Baranov, Yurii Belov
Publication date: 25 October 2020
Abstract: We study hereditary completeness of systems of exponentials on an interval such that the corresponding generating function $G$ is small outside of a lacunary sequence of intervals $I_k$. We show that, under some technical conditions, an exponential system is hereditarily complete if and only if the logarithmic length of the union of these intervals is infinite, i.e., $sum_kint_{I_k} frac{dx}{1+|x|}=infty$.
Dirichlet series, exponential series and other series in one complex variable (30B50) Completeness problems, closure of a system of functions of one complex variable (30B60)
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