A non-uniform Datko-Pazy theorem for bounded operator semigroups
Functional Analysis
2024-09-20 v1
Abstract
We present a non-uniform analogue of the classical Datko-Pazy theorem. Our main result shows that an integrability condition imposed on orbits originating in a fractional domain of the generator (as opposed to all orbits) implies polynomial stability of a bounded -semigroup. As an application of this result we establish polynomial stability of a semigroup under a certain non-uniform Lyapunov-type condition. We moreover give a new proof, under slightly weaker assumptions, of a recent result deducing polynomial stability from a certain non-uniform observability condition.
Cite
@article{arxiv.2409.12764,
title = {A non-uniform Datko-Pazy theorem for bounded operator semigroups},
author = {Lassi Paunonen and David Seifert and Nicolas Vanspranghe},
journal= {arXiv preprint arXiv:2409.12764},
year = {2024}
}