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arXiv · 2107.02832

On asymptotics for $C_0$-semigroups

Marat V. Markin
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Abstract

We stretch the spectral bound equal growth bound condition along with a generalized Lyapunov stability theorem, known to hold for $C_0$-semigroups of normal operators on complex Hilbert spaces, to $C_0$-semigroups of scalar type spectral operators on complex Banach spaces. For such semigroups, we obtain exponential estimates with the best stability constants. We also extend to a Banach space setting a celebrated characterization of uniform exponential stability for $C_0$-semigroups on complex Hilbert spaces and thereby acquire a characterization of uniform exponential stability for scalar type spectral and eventually norm-continuous $C_0$-semigroups.

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Marat V. Markin. 2021-07-06. On asymptotics for $C_0$-semigroups. https://arxiv.org/abs/2107.02832

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