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arXiv · 1006.1840

A problem on completeness of exponentials

Alexei Poltoratski
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Abstract

Let $μ$ be a finite positive measure on the real line. For $a>0$ denote by $\EE_a$ the family of exponential functions $$\EE_a=\{e^{ist}| \ s\in[0,a]\}.$$ The exponential type of $μ$ is the infimum of all numbers $a$ such that the finite linear combinations of the exponentials from $\EE_a$ are dense in $L^2(μ)$. If the set of such $a$ is empty, the exponential type of $μ$ is defined as infinity. The well-known type problem asks to find the exponential type of $μ$ in terms of $μ$. \ms\no In this note we present a solution to the type problem and discuss its relations with known results.

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Alexei Poltoratski. 2011-07-06. A problem on completeness of exponentials. https://arxiv.org/abs/1006.1840

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