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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
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.

References [Enhancements On Off] (What's this?)

  • [1] P. L. Butzer and H. Berens, Semi-groups of operators and approximation, Die Grundlehren der math. Wissenchaften, Band 145, Springer-Verlag, Berlin and New York, 1967. MR 37 #5588. MR 0230022 (37:5588)
  • [2] Z. Ditzian, On Hille's first exponential formula, Proc. Amer. Math. Soc. 22 (1969), 351-355. MR 0244804 (39:6118)

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Keywords: Semigroups, modulus of continuity
Article copyright: © Copyright 1970 American Mathematical Society

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