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arXiv · 1804.02374

An abstract approach to optimal decay of functions and operator semigroups

Gregory Debruyne·David Seifert
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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.

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Gregory Debruyne, David Seifert. 2019-07-28. An abstract approach to optimal decay of functions and operator semigroups. https://doi.org/10.1007/s11856-019-1918-y

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