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math.FA2018
Optimality of the quantified Ingham-Karamata theorem for operator semigroups with general resolvent growth
Gregory Debruyne, David Seifert
We prove that a general version of the quantified Ingham-Karamata theorem for -semigroups is sharp under mild conditions on the resolvent growth, thus generalising the results…
math.CA2018
An abstract approach to optimal decay of functions and operator semigroups
Gregory Debruyne, David Seifert
We provide a new and significantly shorter optimality proof of recent quantified Tauberian theorems, both in the setting of vector-valued functions and of -semigroups, and in…
math.AP2018
Optimal energy decay for the wave-heat system on a rectangular domain
Charles Batty, Lassi Paunonen, David Seifert
We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of -semigroups, and in particular a wel…