Generation theorems for $\varphi$ Hille-Yosida operators
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- by Sheng Wang Wang PDF
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Abstract:
This paper introduces the concept of $\varphi$ Hille-Yosida operators and studies several generation theorems. We show that if a once-integrated semigroup $\{S(t) \}_{t \geq 0}$ satisfies $\Phi (t) := limsup_{h \rightarrow 0^{+}} \frac {1}{h} ||S(t + h) - S(t)|| < \infty$ for all $t > 0 \ a. e.$, then $\Phi (\cdot )$ is locally bounded on $(0, \infty )$ and exponentially bounded. In addition, some other interesting results are presented.References
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Additional Information
- Sheng Wang Wang
- Affiliation: Department of Mathematics, Nanjing University, Jiangsu 210093, People’s Republic of China
- Email: wang2598@netra.nju.edu.cn
- Received by editor(s): June 7, 2000
- Received by editor(s) in revised form: June 26, 2001
- Published electronically: May 29, 2002
- Communicated by: David R. Larson
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3355-3367
- MSC (2000): Primary 47D05; Secondary 47B40
- DOI: https://doi.org/10.1090/S0002-9939-02-06606-6
- MathSciNet review: 1913015