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A characterization of holomorphic semigroups


Author: Tosio Kato
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
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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 $ \vert\zeta \vert \geqq 1$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0264456-0
Keywords: Semigroup of class $ {C_0}$, holomorphic semigroup, resolvent set, spectral radius, operator calculus, semi-Fredholm operator, index
Article copyright: © Copyright 1970 American Mathematical Society

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