2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136477In this paper we present an extension of the Katznelson-Tzafriri Theorem to the asymptotic behavior of individual solutions of evolution equations $u'(t) =Au(t)+f(t)$. The obtained results do not require the uniform continuity of solutions as well as the well-posedness of the equations. The method of study is based on a recently developed approach to the spectral of functions that is direct and free of C_0-semigroups.This is the revised (and final) version of the version of March 28, 2007. This paper is to appear in the Proceedings of the A.M.SDynamical Systems34G10, 47D06text