Characteristic Conditions for the Generation of $\alpha$-Times Resolvent Families on a Hilbert Space |
Received:July 08, 2009 Revised:April 26, 2010 |
Key Words:
$\alpha$-times resolvent family resolvent rank-1 perturbation relatively-bounded perturbation.
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Fund Project:Supported by the National Natural Science Foundation of China (Grant No.\,10971146). |
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Abstract: |
In 2000, Shi and Feng gave the characteristic conditions for the generation of $C_0$-semigroups on a Hilbert space. In this paper, we will extend them to the generation of $\alpha$-times resolvent operator families. Such characteristic conditions can be applied to show rank-1 perturbation theorem and relatively-bounded perturbation theorem for $\alpha$-times resolvent operator families. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2011.03.005 |
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