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Divided Differences & Restriction Operator on Paley-Wiener Spaces for N-Carleson sequences

Frederic Gaunard 1

(31/12/2010)

We study the restriction operator $R_{\Lambda}$ defined on Paley-Wiener spaces, for $\Lambda$ being a sequence of complex numbers. Lyubarskii and Seip gave necessary and sufficient conditions for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and some weighted $l^{p}$ space, involving Carleson's and Muckenhoupt's $(A_{p})$ conditions. Here, we deal with N-Carleson sequences (finite unions of disjoint Carleson sequences) and use the methods of Lyubarskii and Seip to give necessary and sufficient conditions for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and some space of sequences, constructed with the help of divided differences. For $p=2$, this caracterization coincides with a result of Avdonin and Ivanov on Riesz bases of divided differences of exponentials in $L^{2}(0,\tau)$.

1 :	Institut de Mathématiques de Bordeaux (IMB)
	CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II

Domaine

:

Mathématiques/Variables complexes

Mots Clés : Interpolation – Divided differences – Paley-wiener spaces – Carleson condition – Discrete muckenhoupt condition

hal-00585565, version 1

http://hal.archives-ouvertes.fr/hal-00585565

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Contributeur : Frederic Gaunard <>

Soumis le : Mercredi 13 Avril 2011, 15:41:21

Dernière modification le : Mercredi 13 Avril 2011, 18:16:03