Optimal polynomial decay of functions and operator semigroups

2009/10/05 by Alexander Borichev, Yuri Tomilov, Borichev, Alexander +1 · 32 citations
Engineering · Mathematics · Computer Science · #Stability and Controllability of Differential Equations #Nonlinear Differential Equations Analysis #Advanced Mathematical Modeling in Engineering

paper · doi:10.1007/s00208-009-0439-0

Abstract

We characterize the polynomial decay of orbits of Hilbert space C₀-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.

Citations

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