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November  2013, 33(11&12): 5203-5216. doi: 10.3934/dcds.2013.33.5203

## Stability estimates for semigroups on Banach spaces

 1 Department of Mathematics, University of Missouri, Columbia, MO 65211, United States

Received  July 2011 Revised  July 2011 Published  May 2013

For a strongly continuous operator semigroup on a Banach space, we revisit a quantitative version of Datko's Theorem and the estimates for the constant $M$ satisfying the inequality $||T(t)|| ≤ M e^{\omega t}$, for all $t\ge0$, in terms of the norm of the convolution and other operators involved in Datko's Theorem. We use techniques recently developed by B. Helffer and J. Sjöstrand for the Hilbert space case to estimate $M$ in terms of the norm of the resolvent of the generator of the semigroup in the right half-plane.
Citation: Yuri Latushkin, Valerian Yurov. Stability estimates for semigroups on Banach spaces. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 5203-5216. doi: 10.3934/dcds.2013.33.5203
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