Inversion of the Laplace transform and generation of Abel summable semigroups

Authors
Bobrowski, A
Citation
A. Bobrowski, Inversion of the Laplace transform and generation of Abel summable semigroups, J FUNCT ANA, 186(1), 2001, pp. 1-24
Citations number
18
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN journal
00221236 → ACNP
Volume
186
Issue
1
Year of publication
2001
Pages
1 - 24
Database
ISI
SICI code
0022-1236(20011020)186:1<1:IOTLTA>2.0.ZU;2-0
Abstract
Necessary and sufficient conditions are given for a Banach-space-valued fun ction f to be the Laplace-Stieltjes transform of a function of bounded vari ation. These conditions are used to obtain generation theorems for both abs olutely continuous integrated semigroups and Abel summable semigroups. (C) 2001 Academic Press.