Resolvent estimates and rates of decay of operator semigroups

For some time now there has been considerable interest, often motivated by applications to the study of energy decay of damped waves, in results which allow one to convert a resolvent estimate for a semigroup generator into a rate of decay for the associated semigroup. In this talk I shall survey some of the main results in this area, including a recent optimal result in the Hilbert space setting. If time permits I may also outline an abstract approach to obtaining resolvent estimates for a general class of second-order systems which can be used to study not only damped waves but also damped (fractional) Klein-Gordon equations and damped beam equations. The talk is based on joint work with Ralph Chill, Lassi Paunonen, Jan Rozendaal, Reinhard Stahn and Yuri Tomilov.

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