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Generation theorems for $\varphi $ Hille-Yosida operators

Author: Sheng Wang Wang
Journal: Proc. Amer. Math. Soc. 130 (2002), 3355-3367
MSC (2000): Primary 47D05; Secondary 47B40
Published electronically: May 29, 2002
MathSciNet review: 1913015
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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 $t > 0 a. e.$, then $\Phi (\cdot )$ is locally bounded on $(0, \infty )$ and exponentially bounded. In addition, some other interesting results are presented.

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Additional Information

Sheng Wang Wang
Affiliation: Department of Mathematics, Nanjing University, Jiangsu 210093, People’s Republic of China

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
Article copyright: © Copyright 2002 American Mathematical Society

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