Comptes Rendus
Harmonic Analysis
Uniqueness sets for unbounded spectra
[Ensembles dʼunicité pour des spectres non-bornés]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 679-681.

Pour tout ensemble SR de mesure finie nous construisons un système dʼexponentielles {eiλt}λΛ qui est total dans L2(S) et dont lʼensemble des fréquences a la densité critique, à savoir mes(S)/2π.

For every set SR of finite measure, we construct a system of exponentials {eiλt}λΛ which is complete in L2(S) and such that the set of frequencies Λ has the critical density D(Λ)=mes(S)/2π.

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Accepté le :
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DOI : 10.1016/j.crma.2011.05.010

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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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/

[1] W.O. Amrein; A.M. Berthier On support properties of Lp-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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