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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Spectral theory for contraction semigroups on Hilbert space

Author: Larry Gearhart
Journal: Trans. Amer. Math. Soc. 236 (1978), 385-394
MSC: Primary 47D05
MathSciNet review: 0461206
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Abstract: In this paper we determine the relationship between the spectra of a continuous contraction semigroup on Hilbert space and properties of the resolvent of its infinitesimal generator. The methods rely heavily on dilation theory. In particular, we reduce the general problem to the case that the cogenerator of the semigroup has a characteristic function with unitary boundary values. We then complete the analysis by generalizing the scalar result of J. W. Moeller on compressions of the translation semigroup to the case of infinite multiplicity.

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Article copyright: © Copyright 1978 American Mathematical Society