Geodesic
On the spectral mapping theorem for a one-parameter group of operators
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 146-150

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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: $\sigma(U(t))=\overline{\exp(\sigma(A)t)}$. 
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     author = {Vu Quok Phong and Yu. I. Lyubich},
     title = {On the spectral mapping theorem for a one-parameter group of operators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {146--150},
     publisher = {mathdoc},
     volume = {178},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a5/}
}
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Vu Quok Phong; Yu. I. Lyubich. On the spectral mapping theorem for a one-parameter group of operators. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 146-150. http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a5/