Comptes Rendus
Harmonic Analysis
Revisiting Landauʼs density theorems for Paley–Wiener spaces
[Retour sur les théorèmes de densité de Landau dans les espaces de Paley–Wiener]
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
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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/

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[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

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[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

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Research supported in part by Israel Science Foundation.

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