Spectral theorem for unbounded strongly continuous groups on a Hilbert space

Authors:
Khristo Boyadzhiev and Ralph deLaubenfels

Journal:
Proc. Amer. Math. Soc. **120** (1994), 127-136

MSC:
Primary 47D03; Secondary 47A60

DOI:
https://doi.org/10.1090/S0002-9939-1994-1186983-0

MathSciNet review:
1186983

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose is a closed, densely defined linear operator on a Hilbert space and . Denote by .

We show that has an functional calculus, for all , if and only if generates a strongly continuous group of operators of exponential type . We obtain specific upper bounds on , in terms of .

Corollaries include the spectral theorem for closed operators on a Hilbert space and a generalization of a result due to McIntosh relating imaginary powers and functional calculi.

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1186983-0

Article copyright:
© Copyright 1994
American Mathematical Society