On the spectrum of 𝐶₀-semigroups

Prüss, Jan

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

On the spectrum of $C_{0}$-semigroups
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by Jan Prüss PDF

Trans. Amer. Math. Soc. 284 (1984), 847-857 Request permission

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 $(\ast )\;u’ = Au + f$ 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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