Powers of generators of holomorphic semigroups

We show that when the (possibly unbounded) linear operator −A- A generates a bounded holomorphic semigroup of angle θ\theta, and n(π/2−θ)>π/2n\left ( {\pi /2 - \theta } \right ) > \pi /2, then −An- {A^n} generates a bounded holomorphic semigroup of angle π/2−n(π/2−θ)\pi /2 - n\left ( {\pi /2 -...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1987-01, Vol.99 (1), p.105-108
Main Author: deLaubenfels, Ralph
Format: Article
Language:English
Subjects:
Mathematical theorems
Mathematics
Research article
Semigroups
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Summary:We show that when the (possibly unbounded) linear operator −A- A generates a bounded holomorphic semigroup of angle θ\theta, and n(π/2−θ)>π/2n\left ( {\pi /2 - \theta } \right ) > \pi /2, then −An- {A^n} generates a bounded holomorphic semigroup of angle π/2−n(π/2−θ)\pi /2 - n\left ( {\pi /2 - \theta } \right ). When −A- A generates a bounded holomorphic semigroup of angle π/2\pi /2, then, for all nn, −An- {A^n} generates a bounded holomorphic semigroup of angle π/2\pi /2.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1987-0866437-5