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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fractional powers of momentum of a spectral distribution


Author: M. Jazar
Journal: Proc. Amer. Math. Soc. 123 (1995), 1805-1813
MSC: Primary 47D03; Secondary 35J10, 35P05, 47A60, 47N20
MathSciNet review: 1242090
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Abstract: In this paper we construct fractional and imaginary powers for the positive momentum B of a spectral distribution and prove the basic properties.

The main result is that for any $ \alpha > 0, - {B^\alpha }$ generates a bounded strongly continuous holomorphic semigroup of angle $ \frac{\pi }{2}$. In particular for $ \alpha = 1$, using Stone's generalized theorem, if iB generates a k-times integrated group of type $ O(\vert t{\vert^k})$ with $ \sigma (B) \subset [0, + \infty [$, then -B generates a strongly continuous holomorphic semigroup of angle $ \frac{\pi }{2}$. A similar corollary is given in the regularized group situation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1242090-0
PII: S 0002-9939(1995)1242090-0
Article copyright: © Copyright 1995 American Mathematical Society