Comptes Rendus
no. 15-16
Harmonic Analysis
Measures with uniformly discrete support and spectrum
[Mesures à support et spectre uniformément discrets]

Présenté par : Jean-Pierre Kahane

Nir Lev1 ; Alexander Olevskii2
1 Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
2 School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
Comptes Rendus. Mathématique, Volume 351 (2013) no. 15-16, pp. 599-603.

Nous caractérisons les mesures sur R ayant toutes les deux leurs support et spectre uniformément discrets. Un résultat similaire est obtenu dans Rn sous une restriction de discrétion plus forte.

We characterize the measures on R which have both their support and spectrum uniformly discrete. A similar result is obtained in Rn under a stronger discreteness restriction.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.09.007
Nir Lev 1 ; Alexander Olevskii 2

1 Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
2 School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel 
@article{CRMATH_2013__351_15-16_599_0,
     author = {Nir Lev and Alexander Olevskii},
     title = {Measures with uniformly discrete support and spectrum},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {599--603},
     publisher = {Elsevier},
     volume = {351},
     number = {15-16},
     year = {2013},
     doi = {10.1016/j.crma.2013.09.007},
     language = {en},
}
TY  - JOUR
AU  - Nir Lev
AU  - Alexander Olevskii
TI  - Measures with uniformly discrete support and spectrum
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 599
EP  - 603
VL  - 351
IS  - 15-16
PB  - Elsevier
DO  - 10.1016/j.crma.2013.09.007
LA  - en
ID  - CRMATH_2013__351_15-16_599_0
ER  - 
%0 Journal Article
%A Nir Lev
%A Alexander Olevskii
%T Measures with uniformly discrete support and spectrum
%J Comptes Rendus. Mathématique
%D 2013
%P 599-603
%V 351
%N 15-16
%I Elsevier
%R 10.1016/j.crma.2013.09.007
%G en
%F CRMATH_2013__351_15-16_599_0
Nir Lev; Alexander Olevskii. Measures with uniformly discrete support and spectrum. Comptes Rendus. Mathématique, Volume 351 (2013) no. 15-16, pp. 599-603. doi : 10.1016/j.crma.2013.09.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.09.007/

[1] A. Córdoba La formule sommatoire de Poisson, C. R. Acad. Sci. Paris, Ser. I, Volume 306 (1988), pp. 373-376

[2] A. Córdoba Dirac combs, Lett. Math. Phys., Volume 17 (1989), pp. 191-196

[3] F. Dyson Birds and frogs, Not. Am. Math. Soc., Volume 56 (2009), pp. 212-223

[4] J.-P. Kahane; S. Mandelbrojt Sur lʼéquation fonctionnelle de Riemann et la formule sommatoire de Poisson, Ann. Sci. Éc. Norm. Super., Volume 75 (1958), pp. 57-80

[5] M.N. Kolountzakis; J.C. Lagarias Structure of tilings of the line by a function, Duke Math. J., Volume 82 (1996), pp. 653-678

[6] J.C. Lagarias Meyerʼs concept of quasicrystal and quasiregular sets, Commun. Math. Phys., Volume 179 (1996), pp. 365-376

[7] J.C. Lagarias Mathematical quasicrystals and the problem of diffraction, Directions in Mathematical Quasicrystals, CRM Monogr. Ser., vol. 13, Amer. Math. Soc., Providence, 2000, pp. 61-93

[8] Y. Meyer Nombres de Pisot, nombres de Salem et analyse harmonique, Lect. Notes Math., vol. 117, Springer-Verlag, 1970

[9] Y. Meyer Algebraic Numbers and Harmonic Analysis, N.-Holl. Math. Libr., vol. 2, North-Holland Publishing Co./American Elsevier Publishing Co., Inc., Amsterdam–London/New York, 1972

[10] Y. Meyer Quasicrystals, Diophantine approximation and algebraic numbers, Les Houches, 1994, Springer, Berlin (1995), pp. 3-16

[11] M. Mitkovski; A. Poltoratski Pólya sequences, Toeplitz kernels and gap theorems, Adv. Math., Volume 224 (2010), pp. 1057-1070

[12] R.V. Moody Meyer sets and their duals, Waterloo, ON, 1995 (NATO Adv. Stud. Inst. Ser., Ser. C, Math. Phys. Sci.), Volume vol. 489, Kluwer Acad. Publ., Dordrecht, The Netherlands (1997), pp. 403-441

[13] A. Olevskii; A. Ulanovskii Universal sampling and interpolation of band-limited signals, Geom. Funct. Anal., Volume 18 (2008), pp. 1029-1052

[14] A. Olevskii; A. Ulanovskii On multi-dimensional sampling and interpolation, Anal. Math. Phys., Volume 2 (2012), pp. 149-170

Cité par Sources :

☆ Research supported in part by the Israel Science Foundation.

Commentaires - Politique