Uniqueness sets for unbounded spectra

Olevskii, Alexander; Ulanovskii, Alexander

doi:10.1016/j.crma.2011.05.010

Harmonic Analysis

Uniqueness sets for unbounded spectra
[Ensembles dʼunicité pour des spectres non-bornés]

Présenté par : Jean-Pierre Kahane

Olevskii, Alexander ¹ ; Ulanovskii, Alexander ²

¹ School of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
² Stavanger University, N-4036 Stavanger, Norway

Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 679-681.

Résumé
Abstract

Pour tout ensemble $S \subset R$ de mesure finie nous construisons un système dʼexponentielles ${e^{i λ t}}_{λ \in Λ}$ qui est total dans $L^{2} (S)$ et dont lʼensemble des fréquences a la densité critique, à savoir $mes (S) / 2 π$ .

For every set $S \subset R$ of finite measure, we construct a system of exponentials ${e^{i λ t}}_{λ \in Λ}$ which is complete in $L^{2} (S)$ and such that the set of frequencies Λ has the critical density $D (Λ) = mes (S) / 2 π$ .

Reçu le : 2011-05-13
Accepté le : 2011-05-17
Publié le : 2011-06-01

DOI : 10.1016/j.crma.2011.05.010

Affiliations des auteurs :

Olevskii, Alexander ¹ ; Ulanovskii, Alexander ²

¹ School of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
² Stavanger University, N-4036 Stavanger, Norway

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     title = {Uniqueness sets for unbounded spectra},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {679--681},
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     url = {http://www.numdam.org/articles/10.1016/j.crma.2011.05.010/}
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Olevskii, Alexander; Ulanovskii, Alexander. Uniqueness sets for unbounded spectra. Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 679-681. doi : 10.1016/j.crma.2011.05.010. http://www.numdam.org/articles/10.1016/j.crma.2011.05.010/

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