Comptes Rendus
no. 1
Harmonic analysis
On irregular sampling in Bernstein spaces
[Sur l'échantillonnage irrégulier dans les espaces de Bernstein]

Présenté par : Jean-Pierre Kahane

Alexander Olevskii1 ; Alexander Ulanovskii2
1 School of Mathematics, Tel Aviv University, Israel
2 Institute for Mathematics and Natural Sciences, Stavanger University, Norway
Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 47-50.

Nous obtenons des estimations finales pour les constantes de l'échantillonnage dans les espaces de Bernstein lorsque la densité des échantillons est proche de la valeur critique.

We obtain sharp estimates for the sampling constants in Bernstein spaces when the density of the sampling set is near the critical value.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.10.018
Alexander Olevskii 1 ; Alexander Ulanovskii 2

1 School of Mathematics, Tel Aviv University, Israel
2 Institute for Mathematics and Natural Sciences, Stavanger University, Norway 
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Alexander Olevskii; Alexander Ulanovskii. On irregular sampling in Bernstein spaces. Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 47-50. doi : 10.1016/j.crma.2014.10.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.10.018/

[1] S.N. Bernstein The extension of properties of trigonometric polynomials to entire functions of finite degree, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 12 (1948), pp. 421-444 (in Russian)

[2] A. Beurling Balayage of Fourier–Stieltjes transforms, The Collected Works of Arne Beurling, vol. 2, Harmonic Analysis, Birkhäuser, Boston, USA, 1989

[3] R.P. Boas; A.C. Schaeffer A theorem of Cartwright, Duke Math. J., Volume 9 (1942), pp. 879-883

[4] A. Borichev; K. Gröchenig; Yu. Lyubarskii Frame constants of Gabor frames near the critical density, J. Math. Pures Appl. (9), Volume 94 (2010) no. 2, pp. 170-182 (in English, with French summary)

[5] L.V. Kantorovich; G.P. Akilov Functional Analysis, Pergamon Press, New York, 1982

[6] H.C. Liu; A.J. Macintyre Cartwright's theorem on functions bounded at the integers, Proc. Amer. Math. Soc., Volume 12 (1961), pp. 460-462

[7] A. Olevskii, A. Ulanovskii, Near critical density irregular sampling in Bernstein spaces, Oberwolfach preprints No. 16, 2013.

[8] Al.A. Privalov The growth of the powers of polynomials, and the approximation of trigonometric projectors, Mat. Zametki, Volume 42 (1987) no. 2, pp. 207-214 (in Russian), English translation in Math. Notes, 41, 1–2, 1987, pp. 619-623

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