A characterization of holomorphic semigroups
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- by Tosio Kato
- Proc. Amer. Math. Soc. 25 (1970), 495-498
- DOI: https://doi.org/10.1090/S0002-9939-1970-0264456-0
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Abstract:
A necessary and sufficient condition is given for a one-parameter semigroup $\{ U(t)\} ,\;0 \leqq t < \infty$, of class ${C_0}$ on a Banach space to be holomorphic (of class $H({\Phi _1},\;{\Phi _2})$ for some ${\Phi _1} < 0 < {\Phi _2}$). The condition is expressed in terms of the spectral properties of $U(t) - \zeta$ for small $t > 0$ and for a complex number $\zeta$ with $|\zeta | \geqq 1$.References
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373 J. W. Neuberger Analyticity and quasi-analyticity for one-parameter semi-groups, (to appear).
- Kôsaku Yosida, On the differentiability of semigroups of linear operators, Proc. Japan Acad. 34 (1958), 337–340. MR 98990
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 495-498
- MSC: Primary 47.50
- DOI: https://doi.org/10.1090/S0002-9939-1970-0264456-0
- MathSciNet review: 0264456