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.References
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Additional Information
- Nguyen Van Minh
- Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
- Email: vnguyen@westga.edu
- 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
- © Copyright 2008 American Mathematical Society
- 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
- MathSciNet review: 2373605