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Perturbation theorems for local integrated semigroups. (English) Zbl 1190.47050
Summary: We apply the contraction mapping theorem to establish some bounded and unbounded perturbation theorems concerning nondegenerate local $$\alpha$$-times integrated semigroups. Some unbounded perturbation results of S. W. Wang, M. Y. Wang and Y. Shen [Stud. Math. 170, No. 2, 121–146 (2005; Zbl 1094.47043)] are also generalized. We also establish some growth properties of perturbations of local $$\alpha$$-times integrated semigroups.

##### MSC:
 47D62 Integrated semigroups 47A55 Perturbation theory of linear operators
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