- 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 combined with a recent result about the existence of non-trivial analytic functions exhibiting rapid decay along strips.
- Publication status:
- Peer review status:
- Peer reviewed
- Springer Verlag Publisher's website
- Israel Journal of Mathematics Journal website
- Acceptance date:
- Pubs id:
- Local pid:
- This article has been accepted for publication in Israel Journal of Mathematics.