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

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

Irregular and multi--channel sampling of operators

The classical sampling theorem for bandlimited functions has recently been generalized to apply to so-called bandlimited operators, that is, to operators with band-limited Kohn-Nirenberg symbols. Here, we discuss operator sampling versions of two of the most central extensions to the classical sampling theorem. In irregular operator sampling, the sampling set is not periodic with uniform distance. In multi-channel operator sampling, we obtain complete information on an operator by multiple operator sampling outputs