English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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, thusgeneralising the results contained in a recent paper by the same authors. Itfollows in particular that the well-known Batty-Duyckaerts theorem is optimaleven for bounded $C_0$-semigroups whose generator has subpolynomial resolventgrowth. Our proof is based on an elegant application of the open mappingtheorem, which we complement by a crucial technical lemma allowing us tostrengthen our earlier results.

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