Mathematical Analysis
Quasicrystals are sets of stable sampling
Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1235-1238.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.10.006
Matei, Basarab 1; Meyer, Yves 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
@article{CRMATH_2008__346_23-24_1235_0,
     author = {Matei, Basarab and Meyer, Yves},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.10.006/}
}
TY  - JOUR
AU  - Matei, Basarab
AU  - Meyer, Yves
TI  - Quasicrystals are sets of stable sampling
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 1235
EP  - 1238
VL  - 346
IS  - 23-24
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.10.006/
DO  - 10.1016/j.crma.2008.10.006
LA  - en
ID  - CRMATH_2008__346_23-24_1235_0
ER  - 
%0 Journal Article
%A Matei, Basarab
%A Meyer, Yves
%T Quasicrystals are sets of stable sampling
%J Comptes Rendus. Mathématique
%D 2008
%P 1235-1238
%V 346
%N 23-24
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.10.006/
%R 10.1016/j.crma.2008.10.006
%G en
%F CRMATH_2008__346_23-24_1235_0
Matei, Basarab; Meyer, Yves. 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. http://www.numdam.org/articles/10.1016/j.crma.2008.10.006/

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

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

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

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

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

Cited by Sources: