Resumen de Admissibility in the Strong and Weak Senses

Luis Barreira, Clàudia Valls Anglès

• For a dynamics with continuous time determined by a nonautonomous linear equation, we characterize completely the notion of an exponential dichotomy with respect to a family of norms in terms of an admissibility property. Moreover, we consider both strong and weak admissibility properties, which are expressed, respectively, in terms of classical and mild solutions. As a nontrivial application, we establish the robustness of the notions of an exponential dichotomy with respect to a family of norms and of a nonuniform exponential dichotomy in a very simple manner.