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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0883409-5
PII: S 0002-9939(1987)0883409-5
Article copyright: © Copyright 1987 American Mathematical Society