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The Hille-Yosida and Trotter-Kato theorems for integrated semigroups. (English) Zbl 0791.47035
Summary: We completely characterize the generators of non-degenerate exponentially bounded \(n\)-times integrated semigroups. We deduce some perturbation results. We also give a proof of the Trotter-Kato theorem inspired from the classical one.

MSC:
47D06 One-parameter semigroups and linear evolution equations
47A55 Perturbation theory of linear operators
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