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Generation theorems for Hille-Yosida operators
Authors:Sheng Wang Wang
Affiliation:Department of Mathematics, Nanjing University, Jiangsu 210093, People's Republic of China
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} vertvert S(t + h) - S(t)vertvert < 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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