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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- 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 https://doi.org/10.1090/S0002-9939-1969-0244804-X
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47.50
Retrieve articles in all journals with MSC: 47.50
Additional Information
Keywords:
Semigroups,
modulus of continuity
Article copyright:
© Copyright 1970
American Mathematical Society