Proceedings of the American Mathematical Society

Author(s): Sheng Wang Wang
Journal: Proc. Amer. Math. Soc. 130 (2002), 3355-3367.
MSC (2000): Primary 47D05; Secondary 47B40
Posted: May 29, 2002
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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 $\Phi (t) := limsup_{h \rightarrow 0^{+}} \frac{1}{h} \vert\vert S(t + h) - S(t)\vert\vert < \infty$ for all

, then $\Phi (\cdot )$ is locally bounded on $(0, \infty )$ and exponentially bounded. In addition, some other interesting results are presented.

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