Divided Differences & Restriction Operator on Paley-Wiener Spaces $PW_{tau}^{p}$ for $N-$Carleson Sequences

For a sequence of complex numbers $Λ$ we consider the restriction operator $R_Λ$ defined on Paley-Wiener spaces $PW_τ^{p}$ ($1<p<\infty$). Lyubarskii and Seip gave necessary and sufficient conditions on $Λ$ for $R_Λ$ to be an isomorphism between $PW_τ^{p}$ and a certain weighted $l^{p}$ space. The Carleson condition appears to be necessary. We extend their result to $N-$Carleson sequences (finite unions of $N$ disjoint Carleson sequences). More precisely, we give necessary and sufficient conditions for $R_Λ$ to be an isomorphism between $PW_τ^{p}$ and an appropriate sequence space involving divided differences.

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