A Spectral Theory of Non-Uniformly Continuous Functions and the Loomis-Arendt-Batty-Vu Theory on the Asymptotic Behavior of Solutions of Evolution Equations

Mathematics – Functional Analysis

Scientific paper

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23 pages

Scientific paper

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.

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