A remark on cosine families

Rankin, Samuel M.

doi:10.1090/S0002-9939-1980-0567976-0

A remark on cosine families
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by Samuel M. Rankin PDF

Proc. Amer. Math. Soc. 79 (1980), 376-378 Request permission

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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On operator-valued solutions of d’Alemberts’ functional equation

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