Anzeige
Erschienen in:
2015 | OriginalPaper | Buchkapitel
Estimates on Non-uniform Stability for Bounded Semigroups
verfasst von : Thomas Duyckaerts
Erschienen in: Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Let S(t) be a bounded strongly continuous semigroup on a Banach space, with generator −A. Assume that the spectrum of A has empty intersection with the imaginary axis. In [6], Charles J.K. Batty and the author have given an estimate of the decay of the operator norm of $$S(t)(1+A)^{-1}$$ , as t tends to infinity, in terms of asymptotic bounds of the resolvent of A on the imaginary axis. In this note, we give another proof of this result. The original proof relied on a trick appearing in an analytic proof of the prime number theorem by D. Newman, which we do not use here.