Non-uniform stability for bounded semi-groups on Banach spaces

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Stability of Operators and Operator Semigroups (2010, result): “As some recent contributions we mention papers by Batkai, Engel, Prüss, Schnaubelt [20], Batty, Duyckaerts [25] and Borichev, Tomilov [39] on polynomial decay of the orbits and Chill, Tomilov [49] on characterisations of strong stability on Banach spaces with Fourier type.”
Sharp polynomial decay rates for the damped wave equation on the torus (2012, background): “3] yield that m1(t) ≥ C (1+t)2/3 , for some C > 0 (with the notation of [BD08] where m1(t) denotes the best decay rate).”
Fine scales of decay of operator semigroups (2013, methodology): “The study of rates was put into the setting of Tauberian theorems for Laplace transforms in [13], by regarding the resolvent as the Laplace transform of the semigroup and partially inverting the Laplace transform.”
Stabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditions (2019, background): “4 of [12] (see also [9, 10, 20]) that we partially recall.”