Comptes Rendus
no. 13-14
Harmonic Analysis
On Ingham-type interpolation in Rn
Presented by: Jean-Pierre Kahane
Alexander Olevskii1; Alexander Ulanovskii2
1School of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Israel
2Stavanger University, 4036 Stavanger, Norway
Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 807-810

Let S and K be 0-symmetric convex bodies in Rn. We are interested in determining conditions under which every set Λ satisfying (Λ−Λ)∩K={0} is a set of interpolation for the Paley–Wiener space of functions with spectrum in S. Some sufficient and necessary conditions are given which, in particular, imply sharp asymptotic estimates for the lp-balls.

Soient S et K deux ensembles convexes 0-symétriques (symétriques par rapport à 0). A quelle condition tout ensemble Λ vérifiant (Λ−Λ)∩K={0} est-il un ensemble d'interpolation pour les fonctions localement L2 à spectre dans S ? On donne des conditions nécessaires et des conditions suffisantes pour qu'il en soit ainsi, et on en dérive des estimations précises pour les boules lp quand n→∞.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.06.007

Alexander Olevskii  1 ; Alexander Ulanovskii  2

1 School of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Israel
2 Stavanger University, 4036 Stavanger, Norway 
@article{CRMATH_2010__348_13-14_807_0,
     author = {Alexander Olevskii and Alexander Ulanovskii},
     title = {On {Ingham-type} interpolation in $ {\mathbb{R}}^{n}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {807--810},
     year = {2010},
     publisher = {Elsevier},
     volume = {348},
     number = {13-14},
     doi = {10.1016/j.crma.2010.06.007},
     language = {en},
}
TY  - JOUR
AU  - Alexander Olevskii
AU  - Alexander Ulanovskii
TI  - On Ingham-type interpolation in $ {\mathbb{R}}^{n}$
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 807
EP  - 810
VL  - 348
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2010.06.007
LA  - en
ID  - CRMATH_2010__348_13-14_807_0
ER  - 
%0 Journal Article
%A Alexander Olevskii
%A Alexander Ulanovskii
%T On Ingham-type interpolation in $ {\mathbb{R}}^{n}$
%J Comptes Rendus. Mathématique
%D 2010
%P 807-810
%V 348
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2010.06.007
%G en
%F CRMATH_2010__348_13-14_807_0
Alexander Olevskii; Alexander Ulanovskii. On Ingham-type interpolation in $ {\mathbb{R}}^{n}$. Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 807-810. doi: 10.1016/j.crma.2010.06.007

[1] J.W.S. Cassels An Introduction to the Geometry of Numbers, Springer-Verlag, 1971

[2] A.E. Ingham Some trigonometrical inequalities with applications in the theory of series, Math. Z., Volume 41 (1936) no. 1, pp. 367-379

[3] J.-P. Kahane Fonctions pseudo-périodiques dans Rp (French), Jerusalem, 1960, Jerusalem Academic Press/Pergamon, Jerusalem/Oxford (1961), pp. 274-281

[4] J.-P. Kahane Pseudopériodicité et séries de Fourier lacunaires, Ann. Sci. Ecole Norm. Sup. (3), Volume 79 (1962), pp. 93-150

[5] V. Komornik; P. Loreti Fourier Series in Control Theory, Springer Monographs in Mathematics, Springer-Verlag, 2005

Cited by Sources:

Comments - Policy