Katznelson-Tzafriri type theorems for individual solutions of evolution equations

Minh, Nguyen

doi:10.1090/S0002-9939-08-09330-1

Katznelson-Tzafriri type theorems for individual solutions of evolution equations
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by Nguyen Van Minh PDF

Proc. Amer. Math. Soc. 136 (2008), 1749-1755 Request permission

Corrigendum: Proc. Amer. Math. Soc. 138 (2010), 2263-2263.

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 theory of functions that is direct and free of $C_0$-semigroups.

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