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On perturbation of \(K\)-regularized resolvent families. (English) Zbl 1051.45009

The authors introduce the notion of a \(k\)-regularized resolvent family, being a resolvent family satisfying a given Volterra integral equation, and express the generator of the resolvent family in terms of the kernel function \(k\), specialize the result for \(\alpha\)-integrated semigroup generators, and derive an additive perturbation result.

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
47D62 Integrated semigroups
45D05 Volterra integral equations
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