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Zbl 0689.47014
Kellerman, Hermann; Hieber, Matthias
Integrated semigroups. (English)
[J] J. Funct. Anal. 84, No.1, 160-180 (1989). ISSN 0022-1236

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.
[D.Somasundaram]

MSC 2000:: *47D03 (Semi)groups of linear operators

Keywords: resolvents of positive operators; integrated semigroup of a family of bounded operators; structure theory of integrated semigroups; Hille- Yosida condition; generators of locally Lipschitz continuous integrated semigroups; inhomogeneous Cauchy problem; bounded perturbations of generators of integrated semigroups

Cited in: Zbl 1229.47062 Zbl 1068.47053 Zbl 1051.47036 Zbl 0983.47031 Zbl 0833.47034 Zbl 0788.47037 Zbl 0746.47019 Zbl 0698.47025

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