Uniqueness sets for unbounded spectra

Alexander Olevskii; Alexander Ulanovskii

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

Alexander Olevskii ¹ ; Alexander Ulanovskii ²

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

Comptes Rendus. Mathématique, Volume 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 :

Alexander Olevskii ¹ ; Alexander Ulanovskii 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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     author = {Alexander Olevskii and Alexander Ulanovskii},
     title = {Uniqueness sets for unbounded spectra},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {679--681},
     publisher = {Elsevier},
     volume = {349},
     number = {11-12},
     year = {2011},
     doi = {10.1016/j.crma.2011.05.010},
     language = {en},
}

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Alexander Olevskii; Alexander Ulanovskii. Uniqueness sets for unbounded spectra. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 679-681. doi : 10.1016/j.crma.2011.05.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.05.010/

Bibliographie
Cité par

[1] W.O. Amrein; A.M. Berthier On support properties of $L^{p}$ -functions and their Fourier transforms, J. Funct. Anal., Volume 24 (1977) no. 3, pp. 258-267

[2] M. Benedicks On Fourier transforms of functions supported on sets of finite Lebesgue measure, J. Math. Anal. Appl., Volume 106 (1985) no. 1, pp. 180-183

[3] A. Beurling; P. Malliavin On the closure of characters and the zeros of entire functions, Acta Math., Volume 118 (1967), pp. 79-93

[4] H.J. Landau A sparse regular sequence of exponentials closed on large sets, Bull. Amer. Math. Soc., Volume 70 (1964), pp. 566-569

[5] A. Olevskii; A. Ulanovskii Universal sampling and interpolation of band-limited signals, Geom. Funct. Anal., Volume 18 (2008) no. 3, pp. 1029-1052

[6] A. Olevskii; A. Ulanovskii Interpolation in Bernstein and Paley–Wiener spaces, J. Funct. Anal., Volume 256 (2009) no. 10, pp. 3257-3278

[7] A. Olevskii; A. Ulanovskii Approximation of discrete functions and size of spectrum, St. Petersburg Math. J., Volume 21 (2010), pp. 1015-1025

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