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Integrated semigroups. (English) Zbl 0689.47014
W. Arendt in his investigation on resolvents of positive operators introduced the concept of integrated semigroup of a family of bounded operators. Using this concept of integrated semigroups the authors study the structure theory of integrated semigroups and characterise the operators satisfying the Hille-Yosida condition as generators of locally Lipschitz continuous integrated semigroups. As an application, the authors give an easy proof of a theorem due Da Prato and Sinestrari on the inhomogeneous Cauchy problem associated to such operators. In the end the authors consider the bounded perturbations of generators of integrated semigroups.
Reviewer: D.Somasundaram

MSC:
47D03(Semi)groups of linear operators