Necessary and sufficient condition for boundedness of translation operator in de Branges spaces

• Bellavita, Carlo ^[1]
  1. [1] University of Milan

     University of Milan

     Milán, Italia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 3, 2023, págs. 795-815
• Idioma: inglés
• DOI: 10.1007/s13348-022-00373-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • In the previous work Bellavita (Complex Anal. Oper. Theory 15: 96, 2021) we found some necessary conditions for the boundedness of the translation operator T_\zeta in the de Branges space {{\mathcal {H}}}(E). In that case we made use of the Carleson measures for the associated model space. In this work we start from the Pancherel-Polya inequality in the Paley-Wiener space and from the Bernstein inequality in the de Branges space. This different approach allows us to obtain a new condition, in some cases necessary and sufficient, for the boundedness of T_\zeta in the de Branges space.