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Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution Equations

Nguyen Van Minh
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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 C_0-semigroups.

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Nguyen Van Minh. 2007-08-22. Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution Equations. https://arxiv.org/abs/math/0703852

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