Local spectra and individual stability of uniformly bounded $C_0$-semigroups
Open Access
- 1 May 1998
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 350 (5) , 2071-2085
- https://doi.org/10.1090/s0002-9947-98-01919-9
Abstract
We study the asymptotic behaviour of individual orbits $T(\cdot )x$ of a uniformly bounded $C_{0}$-semigroup $\{T(t) \}_{t\ge 0}$ with generator $A$ in terms of the singularities of the local resolvent $(\lambda -A)^{-1} x$ on the imaginary axis. Among other things we prove individual versions of the Arendt-Batty-Lyubich-Vũ theorem and the Katznelson-Tzafriri theorem.
Keywords
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