Generation theorems for 𝜑 Hille-Yosida operators

Wang, Sheng

doi:10.1090/S0002-9939-02-06606-6

Generation theorems for $\varphi$ Hille-Yosida operators
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by Sheng Wang Wang PDF

Proc. Amer. Math. Soc. 130 (2002), 3355-3367 Request permission

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.

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