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

Abstract

For a sequence of complex numbers $\Lambda$ we consider the restriction operator $R_{\Lambda }$ defined on Paley-Wiener spaces $P{W}_{\tau }^p$ ($1<p<\infty$). Lyubarskii and Seip gave necessary and sufficient conditions on $\Lambda$ for $R_{\Lambda }$ to be an isomorphism between $P{W}_{\tau }^p$ 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 $R_{\Lambda }$ to be an isomorphism between $P{W}_{\tau }^p$ and an appropriate sequence space involving divided differences.

Cited by in corpus (1)

• von Neumann indices and classes of positive definite functions