2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224977In this paper we present a new approach to the spectral theory of {\it non-uniformly continuous} functions and a new framework for the Loomis-Arendt-Batty-Vu theory. Our approach is direct and free of $C_0$-semigroups, so the obtained results, that extend previous ones, can be applied to large classes of evolution equations and their solutions.23 pagesFunctional AnalysisDynamical Systems34C27; 34D20; 34G10; 35B15; 35B35; 47D06text