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arXiv · 1812.10978

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

Gregory Debruyne·David Seifert
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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.

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Gregory Debruyne, David Seifert. 2018-12-28. Optimality of the quantified Ingham-Karamata theorem for operator semigroups with general resolvent growth. https://doi.org/10.1007/s00013-019-01380-z

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