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An abstract approach to optimal decay of functions and 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:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s11856-019-1918-y

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St John's College
Role:
Author
ORCID:
0000-0002-4076-860X
Publisher:
Springer Verlag
Journal:
Israel Journal of Mathematics More from this journal
Volume:
233
Pages:
439-451
Publication date:
2019-08-19
Acceptance date:
2018-12-23
DOI:
EISSN:
1565-8511
ISSN:
0021-2172
Language:
English
Keywords:
Pubs id:
pubs:894518
UUID:
uuid:ceb0db72-05dc-4de8-9183-bd2bf52800d9
Local pid:
pubs:894518
Source identifiers:
894518
Deposit date:
2018-12-30

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