Journal article

### Optimality of the quantified Ingham-Karamata theorem for operator semigroups with general resolvent growth

Abstract:

We prove that a general version of the quantified Ingham-Karamata theorem for $C_0$-semigroups is sharp under mild conditions on the resolvent growth, thus generalising the results contained in a recent paper by the same authors. It follows in particular that the well-known Batty-Duyckaerts theorem is optimal even for bounded $C_0$-semigroups whose generator has subpolynomial resolvent growth. Our proof is based on an elegant application of the open mapping theorem, which we complement by a c...

Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

### Access Document

Files:
• (pdf, 352.5KB)
Publisher copy:
10.1007/s00013-019-01380-z

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Johns College
Role:
Author
ORCID:
0000-0002-4076-860X
Publisher:
Springer Publisher's website
Journal:
Archiv der Mathematik Journal website
Publication date:
2019-09-11
Acceptance date:
2019-08-11
DOI:
EISSN:
9876-1234
ISSN:
1234-1234
Pubs id:
pubs:957829
URN:
uri:a15f48b1-22b6-4230-aeaf-36cf438d9821
UUID:
uuid:a15f48b1-22b6-4230-aeaf-36cf438d9821
Local pid:
pubs:957829
Keywords: