Journal article

### Optimal decay of functions and one-parameter operator semigroups

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 combined with a recent result about the existence of non-trivial analytic functions exhibiting rapid decay along strips.
Publication status:
Accepted
Peer review status:
Peer reviewed

### Authors

Debruyne, G More by this author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Johns College
ORCID:
0000-0002-4076-860X
Publisher:
Springer Verlag Publisher's website
Journal:
Israel Journal of Mathematics Journal website
Acceptance date:
2018-12-23
EISSN:
1565-8511
ISSN:
0021-2172
Pubs id:
pubs:894518
URN:
uri:ceb0db72-05dc-4de8-9183-bd2bf52800d9
UUID:
uuid:ceb0db72-05dc-4de8-9183-bd2bf52800d9
Local pid:
pubs:894518
Keywords: