On asymptotics for $C_0$-semigroups
Abstract
We stretch the spectral bound equal growth bound condition along with a generalized Lyapunov stability theorem, known to hold for -semigroups of normal operators on complex Hilbert spaces, to -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 -semigroups on complex Hilbert spaces and thereby acquire a characterization of uniform exponential stability for scalar type spectral and eventually norm-continuous -semigroups.
Cite
@article{arxiv.2107.02832,
title = {On asymptotics for $C_0$-semigroups},
author = {Marat V. Markin},
journal= {arXiv preprint arXiv:2107.02832},
year = {2021}
}
Comments
Various readability improvements. There is a text overlap with arXiv:2002.09087 in the Preliminaries section containing introductory information, definitions, and general remarks. arXiv admin note: substantial text overlap with arXiv:2002.09087