## 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.## References

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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