Laplace transforms of polynomially bounded vector-valued functions and semigroups of operators

For any natural numberk, we characterize once-integrated Laplace transforms ofO((1+t)k) andO(tk) Banach-space-valued functions. We use this to give Hille-Yosida type characterizations of generators of polynomially bounded strongly continuous semigroups, related families of operators, and solutions o...

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Bibliographic Details
Published in:Israel journal of mathematics 1997-12, Vol.98 (1), p.189-207
Main Authors: DeLaubenfels, R., Huang, Z., Wang, S., Wang, Y.
Format: Article
Language:English
Subjects:
Cauchy problems
Laplace transforms
Mathematics
Operators (mathematics)
Semigroups
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Summary:For any natural numberk, we characterize once-integrated Laplace transforms ofO((1+t)k) andO(tk) Banach-space-valued functions. We use this to give Hille-Yosida type characterizations of generators of polynomially bounded strongly continuous semigroups, related families of operators, and solutions of the abstract Cauchy problem.
ISSN:0021-2172
1565-8511
DOI:10.1007/BF02937334