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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the spectrum of $ C\sb{0}$-semigroups


Author: Jan Prüss
Journal: Trans. Amer. Math. Soc. 284 (1984), 847-857
MSC: Primary 47D05; Secondary 34G10
MathSciNet review: 743749
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Abstract: In this paper we give characterizations of the spectrum of a $ {C_0}$-semigroup $ {e^{At}}$ in terms of certain solution properties of the differential equation $ (\ast)\;u^{\prime} = Au + f$ and, in case $ X$ is a Hilbert space, also in terms of properties of $ {(\lambda - A)^{ - 1}}$. We give several applications of these results including a study of the existence of dichotomic projections for $ (\ast)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0743749-9
PII: S 0002-9947(1984)0743749-9
Keywords: Semigroups, spectrum, periodic solutions, dichotomic projections
Article copyright: © Copyright 1984 American Mathematical Society