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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.


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