Abstract
Abstract
We prove that a general version of the quantified Ingham–Karamata theorem for $$C_0$$C0-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 $$C_0$$C0-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.
Funder
Fonds Wetenschappelijk Onderzoek
Publisher
Springer Science and Business Media LLC
Cited by
4 articles.
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