Geodesic
A problem on completeness of exponentials
Alexei Poltoratski1
1 Texas A&M University, College Station, TX
Annals of mathematics, Tome 178 (2013) no. 3, pp. 983-1016.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $\mu$ be a finite positive measure on the real line. For $a>0$, denote by $\mathcal{E}_a$ the family of exponential functions $$\mathcal{E}_a=\{e^{ist}| s\in[0,a]\}.$$ The exponential type of $\mu$ is the infimum of all numbers $a$ such that the finite linear combinations of the exponentials from $\mathcal{E}_a$ are dense in $L^2(\mu)$. If the set of such $a$ is empty, the exponential type of $\mu$ is defined as infinity. The well-known type problem asks to find the exponential type of $\mu$ in terms of $\mu$. In this note we present a solution to the type problem and discuss its relations with known results.
DOI : 10.4007/annals.2013.178.3.4

Alexei Poltoratski 1

1 Texas A&M University, College Station, TX 
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Alexei Poltoratski. A problem  on completeness of exponentials. Annals of mathematics, Tome 178 (2013) no. 3, pp. 983-1016. doi : 10.4007/annals.2013.178.3.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.3.4/

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