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

Nitzan, Shahaf1 ; Olevskii, Alexander2
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, Tome 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
Nitzan, Shahaf 1 ; Olevskii, Alexander 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 
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Nitzan, Shahaf; Olevskii, Alexander. Revisiting Landauʼs density theorems for Paley–Wiener spaces. Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 509-512. doi : 10.1016/j.crma.2012.05.003. http://www.numdam.org/articles/10.1016/j.crma.2012.05.003/

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

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

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☆ Research supported in part by Israel Science Foundation.