Comptes Rendus
Harmonic Analysis
On Ingham-type interpolation in Rn
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 (ΛΛ)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 (ΛΛ)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.

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
     author = {Alexander Olevskii and Alexander Ulanovskii},
     title = {On {Ingham-type} interpolation in $ {\mathbb{R}}^{n}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {807--810},
     publisher = {Elsevier},
     volume = {348},
     number = {13-14},
     year = {2010},
     doi = {10.1016/j.crma.2010.06.007},
     language = {en},
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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

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