Quasicrystals are sets of stable sampling

Basarab Matei; Yves Meyer

doi:10.1016/j.crma.2008.10.006

Mathematical Analysis

Quasicrystals are sets of stable sampling

Presented by: Yves Meyer

Basarab Matei ¹; Yves Meyer ²

¹ LAGA, Université Paris Nord, 99, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France
² CMLA, ENS-Cachan, 61, avenue du Président-Wilson, 94235 Cachan cedex, France

Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1235-1238.

Abstract
Résumé

Irregular sampling and “stable sampling” of band-limited functions have been studied by H.J. Landau [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52]. We prove that quasicrystals are sets of stable sampling.

Répondant à une question posée par H.J. Landau [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52] sur le problème de l'échantillonnage irrégulier des fonctions “band-limited”, nous prouvons que les quasicristaux sont des ensembles d'échantillonnage stable.

Received: 2008-05-22
Accepted: 2008-10-13
Published online: 2008-10-30

DOI: 10.1016/j.crma.2008.10.006

Author's affiliations:

Basarab Matei ¹; Yves Meyer ²

¹ LAGA, Université Paris Nord, 99, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France
² CMLA, ENS-Cachan, 61, avenue du Président-Wilson, 94235 Cachan cedex, France

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     author = {Basarab Matei and Yves Meyer},
     title = {Quasicrystals are sets of stable sampling},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1235--1238},
     publisher = {Elsevier},
     volume = {346},
     number = {23-24},
     year = {2008},
     doi = {10.1016/j.crma.2008.10.006},
     language = {en},
}

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Basarab Matei; Yves Meyer. Quasicrystals are sets of stable sampling. Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1235-1238. doi : 10.1016/j.crma.2008.10.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.10.006/

References
Cited by

[1] A. Beurling Collected Works of Arne Beurling, 2 vols. (L. Carleson et al., eds.), Birkhäuser, 1989

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

[3] Y. Meyer Nombres de Pisot, nombres de Salem et Analyse Harmonique, Lecture Notes in Mathematics, vol. 117, 1970

[4] Y. Meyer Trois problèmes sur les sommes trigonométriques, Astérisque, vol. 1, SMF, 1973

[5] A. Olevskii; A. Ulanovskii A universal sampling of band-limited signals, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006), pp. 927-931

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