2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61923We present a characterization of hyperbolicity for strongly continuous semigroups on Banach spaces in terms of Fourier multiplier properties of the resolvent of the generator. Hyperbolicity with respect to classical solutions is also considered. Our approach unifies and simplifies the M. Kaashoek-- S. Verduyn Lunel theory and multiplier-type results previously obtained by S. Clark, M. Hieber, S. Montgomery-Smith, F. Räbiger, T. Randolph, and L. Weis.26 pagesFunctional AnalysisPrimary: 47D06; Secondary: 42B15text