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Proceedings of the American Mathematical Society

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On the relation between the semigroup and its infinitesimal generator

Author: Frank Neubrander
Journal: Proc. Amer. Math. Soc. 100 (1987), 104-108
MSC: Primary 47D05; Secondary 44A10
MathSciNet review: 883409
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Abstract: We prove that for a semigroup generator $ A$ the solutions of $ u'(t) = Au(t)$ and $ u(0) = x$ are completely determined by the resolvent of $ A$ along an equidistant sequence $ {({s_0} + nr)_{n \in {\mathbf{N}}}},r \in {\mathbf{R}},{s_0} \in {\mathbf{C}}$, of points in the resolvent set of $ A$.

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Article copyright: © Copyright 1987 American Mathematical Society