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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. LOMI, 1989 Volume 178, Pages 146–150 (Mi znsl4679)

On the spectral mapping theorem for a one-parameter group of operators

Vu Quok Phong, Yu. I. Lyubich


Abstract: Let $A$ be the generator of a strongly continuous non-quasianalytic one-parameter group of operators $U(t)$ ($A$ can be unbounded). Then the spectral mapping theorem is established in the following form: $\sigma(U(t))=\overline{\exp(\sigma(A)t)}$.

UDC: 517.5


 English version:
Journal of Soviet Mathematics, 1992, 61:2, 2035–2037

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