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

• Autores: Frédéric Gaunard
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 64, Fasc. 2, 2013, págs. 251-281
• Idioma: inglés
• DOI: 10.1007/s13348-012-0066-z
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• Resumen

  • 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.