On the spectrum of 𝐶₀-semigroups

Prüss, Jan

doi:10.1090/S0002-9947-1984-0743749-9

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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 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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