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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fractional powers of momentum of a spectral distribution
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by M. Jazar PDF
Proc. Amer. Math. Soc. 123 (1995), 1805-1813 Request permission

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 $O(|t{|^k})$ 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
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1805-1813
  • MSC: Primary 47D03; Secondary 35J10, 35P05, 47A60, 47N20
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242090-0
  • MathSciNet review: 1242090