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Note on Hille's exponential formula


Author: Z. Ditzian
Journal: Proc. Amer. Math. Soc. 25 (1970), 351-352
MSC: Primary 47.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0256209-4
MathSciNet review: 0256209
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Abstract: In an earlier paper of the author it was shown that we would not be able to obtain a better estimate for Hille's first exponential formula than $ K{w_B}({\tau ^{1/2}},T( \cdot )f)$, where $ {w_B}(\delta ,T( \cdot )f)$ is the global modulus of continuity of $ T(t)f,t \in [0,B]$. It is shown in this paper that this estimate can actually be achieved.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0256209-4
Keywords: Semigroups, modulus of continuity
Article copyright: © Copyright 1970 American Mathematical Society

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