Note on Hille’s exponential formula
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- by Z. Ditzian
- Proc. Amer. Math. Soc. 25 (1970), 351-352
- DOI: https://doi.org/10.1090/S0002-9939-1970-0256209-4
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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
- Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York, Inc., New York, 1967. MR 0230022
- Z. Ditzian, On Hille’s first exponential formula, Proc. Amer. Math. Soc. 22 (1969), 351–355. MR 244804, DOI 10.1090/S0002-9939-1969-0244804-X
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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