Laplace transforms and generators of semigroups of operators

Peng, Jigen; Chung, Si-Kit

doi:10.1090/S0002-9939-98-04603-6

Laplace transforms and generators of semigroups of operators
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by Jigen Peng and Si-Kit Chung

Proc. Amer. Math. Soc. 126 (1998), 2407-2416

DOI: https://doi.org/10.1090/S0002-9939-98-04603-6

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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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