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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Laplace Transforms and Generators
of Semigroups of Operators


Authors: Jigen Peng and Si-Kit Chung
Journal: Proc. Amer. Math. Soc. 126 (1998), 2407-2416
MSC (1991): Primary 47D03; Secondary 44A10
MathSciNet review: 1469432
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Abstract: In this paper, a characterization for continuous functions on $(0,\infty)$ to be the Laplace transforms of $f\in L^{\infty}(0,\infty)$ is obtained. It is also shown that the vector-valued version of this characterization holds if and only if the underlying Banach space has the Radon-Nikodým property. Using these characterizations, some results, different from that of the Hille-Yosida theorem, on generators of semigroups of operators are obtained.


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Additional Information

Jigen Peng
Affiliation: Department of Mathematics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China

Si-Kit Chung
Affiliation: Department of Mathematics, Hong Kong University, Hong Kong

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04603-6
PII: S 0002-9939(98)04603-6
Received by editor(s): March 18, 1996
Received by editor(s) in revised form: January 23, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society