Comptes Rendus
Mathematical Analysis/Harmonic Analysis
Quasi-frames of translates
[Systèmes de translatées proches des frames]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 739-742.

Nous construisons une suite réelle Λ uniformément discrète (de pas >0) et même lacunaire, et une fonction gL2(R), telles que le système des translatées {g(tλ)}(λΛ) soit un “quasi-frame” au sens suivant : pour tout q>2 il existe C(q)>0 tel que toute fonction fL2(R) est approchable dans L2(R) par des combinaisons linéaires cλg(tλ) vérifiant (|cλ|q)1/qC(q)f. Cela est impossible quand q=2, selon un résultat de Christensen, Deng et Heil.

We construct uniformly discrete, and even sparse, sequences of translates {g(tλ)} of a single function which have the following frame-type approximation property: for every q>2 there exists C(q) such that every function fL2(R) can be approximated with arbitrary small L2-error by a linear combination cλg(tλ) satisfying the lq-estimate of the coefficients:

{cλ}lqC(q)f.
This cannot be done for q=2, according to a result of Christensen, Deng and Heil.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.04.001

Shahaf Nitzan 1 ; Alexander Olevskii 1

1 School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv, Israel 69978
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Shahaf Nitzan; Alexander Olevskii. Quasi-frames of translates. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 739-742. doi : 10.1016/j.crma.2009.04.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.001/

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Supported in part by the Israel Science Foundation.

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