Optimal polynomial decay of functions and operator semigroups

Understand

We characterize the polynomial decay of orbits of Hilbert space $C_0$-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.
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