  In 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.

Functional Analysis;Dynamical Systems