Optimal polynomial decay of functions and operator semigroups
Functional Analysis
2009-10-07 v1 Analysis of PDEs
Abstract
We characterize the polynomial decay of orbits of Hilbert space -semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in the paper by C.J.K.Batty and T.Duyckaerts, Non-uniform stability for bounded semi-groups on Banach spaces (J. Evol. Eq. 2008), are sharp. This settles a conjecture posed in the paper by C.J.K.Batty and T.Duyckaerts.
Cite
@article{arxiv.0910.0859,
title = {Optimal polynomial decay of functions and operator semigroups},
author = {Alexander Borichev and Yuri Tomilov},
journal= {arXiv preprint arXiv:0910.0859},
year = {2009}
}
Comments
21 pages, to appear in Matematische Annalen