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

Powers of generators of holomorphic semigroups


Author: Ralph deLaubenfels
Journal: Proc. Amer. Math. Soc. 99 (1987), 105-108
MSC: Primary 47D05; Secondary 47B44
MathSciNet review: 866437
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Abstract: We show that when the (possibly unbounded) linear operator $ - A$ generates a bounded holomorphic semigroup of angle $ \theta $, and $ n\left( {\pi /2 - \theta } \right) < \pi /2$, then $ - {A^n}$ generates a bounded holomorphic semigroup of angle $ \pi /2 - n\left( {\pi /2 - \theta } \right)$. When $ - A$ generates a bounded holomorphic semigroup of angle $ \pi /2$, then, for all $ n$, $ - {A^n}$ generates a bounded holomorphic semigroup of angle $ \pi /2$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866437-5
PII: S 0002-9939(1987)0866437-5
Article copyright: © Copyright 1987 American Mathematical Society