Divided Differences & Restriction Operator on Paley-Wiener Spaces for N-Carleson sequences
Résumé
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 $L^{2}(0,\tau)$.
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