Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution Equations
Abstract
In 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 C0-semigroups.
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