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

Carlo Bellavita

• In the previous work Bellavita (Complex Anal. Oper. Theory 15: 96, 2021) we found some necessary conditions for the boundedness of the translation operator Tζ in the de Branges space 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 Tζ in the de Branges space.