Admissibility via Induced Delay Equations

We give a new characterization of the existence of an exponential dichotomy for the class of induced delay equations, introduced recently in Barreira and Valls (JDE 391: 396–484, 2024), in terms of the admissibility of a new pair of Banach spaces. Moreover, as a consequence, we give a new application of the theory of induced delay equations to obtain results for nonautonomous delay equations via autonomous equations.