An abstract approach to optimal decay of functions and operator semigroups

DOI10.1007/S11856-019-1918-YarXiv1804.02374WikidataQ127334185 ScholiaQ127334185MaRDI QIDQ6300032

Publication date: 6 April 2018

Abstract: We provide a new and significantly shorter optimality proof of recent quantified Tauberian theorems, both in the setting of vector-valued functions and of

C_{0}

-semigroups, and in fact our results are also more general than those currently available in the literature. Our approach relies on a novel application of the open mapping theorem.

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Laplace transform (44A10) Tauberian theorems (40E05)

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