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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Spectral theory for contraction semigroups on Hilbert space
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by Larry Gearhart PDF
Trans. Amer. Math. Soc. 236 (1978), 385-394 Request permission

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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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 236 (1978), 385-394
  • MSC: Primary 47D05
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0461206-1
  • MathSciNet review: 0461206