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Katznelson-Tzafriri type theorems for individual solutions of evolution equations


Author: Nguyen Van Minh
Journal: Proc. Amer. Math. Soc. 136 (2008), 1749-1755
MSC (2000): Primary 34G10; Secondary 47D06
DOI: https://doi.org/10.1090/S0002-9939-08-09330-1
Published electronically: January 28, 2008
Corrigendum: Proc. Amer. Math. Soc. 138 (2010), 2263-2263.
MathSciNet review: 2373605
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Nguyen Van Minh
Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
Email: vnguyen@westga.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09330-1
Keywords: Katznelson-Tzafriri Type Theorem, reduced spectrum of a function, asymptotic behavior
Received by editor(s): March 26, 2007
Published electronically: January 28, 2008
Additional Notes: The author thanks the referee for carefully reading the manuscript and for making useful remarks.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2008 American Mathematical Society

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