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Title
Optimal polynomial decay of functions and operator semigroups.
Abstract
We characterize the polynomial decay of orbits of Hilbert space C0-semigroupsin resolvent terms. We also show that results of the same type for generalBanach space semigroups and functions obtained recently in Batty and Duyckaerts(J Evol Eq 8:765-780, 2008) are sharp. This settles a conjecture posed in Batty andDuyckaerts (2008).