Powers of generators of holomorphic semigroups
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- by Ralph deLaubenfels
- Proc. Amer. Math. Soc. 99 (1987), 105-108
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866437-5
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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 $\pi /2$.References
- Jerome A. Goldstein, Some remarks on infinitesimal generators of analytic semigroups, Proc. Amer. Math. Soc. 22 (1969), 91–93. MR 243384, DOI 10.1090/S0002-9939-1969-0243384-2
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419 J. A. van Casteren, Generators of strongly continuous semigroups, Research Notes in Math., 115, Pitman, 1985.
- Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York, Inc., New York, 1968. MR 0239384
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 105-108
- MSC: Primary 47D05; Secondary 47B44
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866437-5
- MathSciNet review: 866437