Divided differences and restriction operator on Paley–Wiener spaces $${PW_{\tau}^{p}}$$ for N–Carleson sequences

Abstract

For a sequence of complex numbers $${\Lambda}$$ we consider the restriction operator $${R_{\Lambda}}$$ defined on Paley–Wiener spaces $${PW_{\tau}^{p}}$$ (1 < p < ∞). 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.