Katznelson-Tzafriri type theorems for individual solutions of evolution equations

DOI10.1090/S0002-9939-08-09330-1zbMath1157.34049arXivmath/0703852OpenAlexW2094524571MaRDI QIDQ5448939

Nguyen Van Minh

Publication date: 10 March 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703852

Mathematics Subject Classification ID

Linear differential equations in abstract spaces (34G10) Asymptotic properties of solutions to ordinary differential equations (34D05) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items (6)

Corrigendum to ‘‘Katznelson-Tzafriri type theorems for individual solutions of evolution equations” ⋮ Circular spectrum and bounded solutions of periodic evolution equations ⋮ Asymptotic behavior of individual orbits of discrete systems ⋮ A spectral theory of continuous functions and the Loomis-Arendt-Batty-Vu theory on the asymptotic behavior of solutions of evolution equations ⋮ On the asymptotic behaviour of Volterra difference equations ⋮ A Katznelson-Tzafriri type theorem for almost periodic linear evolution equations

Cites Work

• A spectral theory of continuous functions and the Loomis-Arendt-Batty-Vu theory on the asymptotic behavior of solutions of evolution equations
• On power bounded operators
• Theorems of Katznelson-Tzafriri type for semigroups of operators
• The asymptotic behaviour of semigroups of linear operators
• Harmonic analysis and asymptotic behavior of solutions to the abstract Cauchy problem
• The Banach algebra generated by a \(C_{0}\)-semigroup
• Bounded Solutions of Parabolic Equations in Continuous Function Spaces
• Vector-Valued Tauberian Theorems and Asymptotic Behavior of Linear Volterra Equations
• Evolutionary Integral Equations and Applications
• Local spectra and individual stability of uniformly bounded $C_0$-semigroups
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