Milán, Italia
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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