Comptes Rendus
no. 9-10
Harmonic Analysis
Revisiting Landauʼs density theorems for Paley–Wiener spaces
[Retour sur les théorèmes de densité de Landau dans les espaces de Paley–Wiener]

Présenté par : Jean-Pierre Kahane

Shahaf Nitzan1 ; Alexander Olevskii2
1 School of Mathematical Sciences, Weizmann Institute for Science, Rehovot 76100, Israel
2 School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv 69978, Israel
Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 509-512.

On présente ici une approche simple, et plutôt surprenante, des théorèmes de densité de Landau fournissant, pour lʼéchantillonnage et lʼinterpolation, des versions plus fortes des résultats connus. En particulier, on étend le théorème dʼinterpolation au spectre non borné.

We present a surprisingly simple approach to Landauʼs density theorems for sampling and interpolation, which provides stronger versions of these results. In particular, we extend the interpolation theorem to unbounded spectra.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.05.003
Shahaf Nitzan 1 ; Alexander Olevskii 2

1 School of Mathematical Sciences, Weizmann Institute for Science, Rehovot 76100, Israel
2 School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv 69978, Israel 
@article{CRMATH_2012__350_9-10_509_0,
     author = {Shahaf Nitzan and Alexander Olevskii},
     title = {Revisiting {Landau's} density theorems for {Paley{\textendash}Wiener} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {509--512},
     publisher = {Elsevier},
     volume = {350},
     number = {9-10},
     year = {2012},
     doi = {10.1016/j.crma.2012.05.003},
     language = {en},
}
TY  - JOUR
AU  - Shahaf Nitzan
AU  - Alexander Olevskii
TI  - Revisiting Landauʼs density theorems for Paley–Wiener spaces
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 509
EP  - 512
VL  - 350
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crma.2012.05.003
LA  - en
ID  - CRMATH_2012__350_9-10_509_0
ER  - 
%0 Journal Article
%A Shahaf Nitzan
%A Alexander Olevskii
%T Revisiting Landauʼs density theorems for Paley–Wiener spaces
%J Comptes Rendus. Mathématique
%D 2012
%P 509-512
%V 350
%N 9-10
%I Elsevier
%R 10.1016/j.crma.2012.05.003
%G en
%F CRMATH_2012__350_9-10_509_0
Shahaf Nitzan; Alexander Olevskii. Revisiting Landauʼs density theorems for Paley–Wiener spaces. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 509-512. doi : 10.1016/j.crma.2012.05.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.05.003/

[1] A. Beurling The Collected Works of Arne Beurling, Contemporary Mathematics, vol. 2, Birkhäuser Boston Inc., Boston, MA, 1989

[2] K. Gröchenig; H. Razafinjatovo On Landauʼs necessary density conditions for sampling and interpolation of band limited functions, J. Lond. Math. Soc., Volume 54 (1996) no. 3, pp. 557-565

[3] J.-P. Kahane Sur les fonctions moyenne-periodiques bornées, Ann. Inst. Fourier, Volume 7 (1957), pp. 293-314

[4] H.J. Landau Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math., Volume 117 (1967), pp. 37-52

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

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

[7] J. Ramanathan; T. Steger Incompleteness of sparse coherent states, Appl. Comput. Harmon. Anal., Volume 2 (1995) no. 2, pp. 148-153

[8] R.M. Young An Introduction to Nonharmonic Fourier Series, Academic Press, 2001

Cité par Sources :

☆ Research supported in part by Israel Science Foundation.

Commentaires - Politique

Ces articles pourraient vous intéresser

Quasi-frames of translates

Shahaf Nitzan; Alexander Olevskii

C. R. Math (2009)

Uniqueness sets for unbounded spectra

Alexander Olevskii; Alexander Ulanovskii

C. R. Math (2011)

Universal sampling of band-limited signals

Alexander Olevskii; Alexander Ulanovskii

C. R. Math (2006)