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 $(\ast )$.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 284 (1984), 847-857
- MSC: Primary 47D05; Secondary 34G10
- DOI: https://doi.org/10.1090/S0002-9947-1984-0743749-9
- MathSciNet review: 743749