Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution Equations

Details Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution Equations Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution Equations

2007-03-28

arxiv.org/abs/math/0703852v2

Mathematics

Dynamical Systems

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.

Scientific paper

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 C_0-semigroups.

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