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.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.\,10971146).
Author NameAffiliation
Rui LIU Department of Mathematics, Sichuan University, Sichuan 610064, P. R. China 
Miao LI Department of Mathematics, Sichuan University, Sichuan 610064, P. R. China 
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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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