Optimality of the quantified Ingham-Karamata theorem for operator semigroups with general resolvent growth

Abstract

We prove that a general version of the quantified Ingham-Karamata theorem for $C_0$-semigroups is sharp under mild conditions on the resolvent growth, thus generalising the results contained in a recent paper by the same authors. It follows in particular that the well-known Batty-Duyckaerts theorem is optimal even for bounded $C_0$-semigroups whose generator has subpolynomial resolvent growth. Our proof is based on an elegant application of the open mapping theorem, which we complement by a crucial technical lemma allowing us to strengthen our earlier results.

arXiv commentTo appear in Archiv der Mathematik

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Cited by in corpus (5)

• Semi-uniform stability of operator semigroups and energy decay of damped waves
• Non-uniform Stability of Damped Contraction Semigroups
• An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions
• Optimal decay of semi-uniformly stable operator semigroups with empty spectrum
• On a space of functions with entire Laplace transforms and its connection with the optimality of the Ingham-Karamata theorem