Harmonic analysis
On irregular sampling in Bernstein spaces

Presented by: Jean-Pierre Kahane

Olevskii, Alexander1; Ulanovskii, Alexander2
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.

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

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.10.018
Olevskii, Alexander 1; Ulanovskii, Alexander 2

1 School of Mathematics, Tel Aviv University, Israel
2 Institute for Mathematics and Natural Sciences, Stavanger University, Norway 
@article{CRMATH_2015__353_1_47_0,
     author = {Olevskii, Alexander and Ulanovskii, Alexander},
     title = {On irregular sampling in {Bernstein} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {47--50},
     publisher = {Elsevier},
     volume = {353},
     number = {1},
     year = {2015},
     doi = {10.1016/j.crma.2014.10.018},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2014.10.018/}
}
TY  - JOUR
AU  - Olevskii, Alexander
AU  - Ulanovskii, Alexander
TI  - On irregular sampling in Bernstein spaces
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 47
EP  - 50
VL  - 353
IS  - 1
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.crma.2014.10.018/
DO  - 10.1016/j.crma.2014.10.018
LA  - en
ID  - CRMATH_2015__353_1_47_0
ER  - 
%0 Journal Article
%A Olevskii, Alexander
%A Ulanovskii, Alexander
%T On irregular sampling in Bernstein spaces
%J Comptes Rendus. Mathématique
%D 2015
%P 47-50
%V 353
%N 1
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2014.10.018/
%R 10.1016/j.crma.2014.10.018
%G en
%F CRMATH_2015__353_1_47_0
Olevskii, Alexander; Ulanovskii, Alexander. 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://www.numdam.org/articles/10.1016/j.crma.2014.10.018/

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

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

[4] Borichev, A.; Gröchenig, K.; Lyubarskii, Yu. 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] Kantorovich, L.V.; Akilov, G.P. Functional Analysis, Pergamon Press, New York, 1982

[6] Liu, H.C.; Macintyre, A.J. 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] Privalov, Al.A. 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

Cited by Sources: