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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A remark on cosine families


Author: Samuel M. Rankin
Journal: Proc. Amer. Math. Soc. 79 (1980), 376-378
MSC: Primary 47D05; Secondary 34G10
DOI: https://doi.org/10.1090/S0002-9939-1980-0567976-0
MathSciNet review: 567976
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Abstract: Let $ C(t),t \in R$, be a strongly continuous cosine family and A its infinitesimal generator. Then the set $ E\stackrel{def}{=}\{ x \in X:C(t)x$ is once continuously differentiable in t on R} of the Banach space X is contained in the domain of $ {( - A)^\alpha }$ for $ 0 \leqslant \alpha < 1/2$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0567976-0
Keywords: Cosine family, semigroup of operators, differential equation
Article copyright: © Copyright 1980 American Mathematical Society