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Interpolation of semigroups and integrated semigroups. (English) Zbl 0782.47035
Krein, Laptev and Cvetkova proved that any operator \(A\) on a Banach space \(E\), the resolvent of which contains a half-line, generates a \(C_ 0\)- semigroup on a certain maximal subspace \(Z\) of \(E\). Generally, no information about the size of \(Z\) is available. The authors of the reviewed paper show that the interesting cases for which \(\text{dom}(A^ k)\subset Z\) are characteristic for generators of \(k\)-times integrated semigroups.

47D06 One-parameter semigroups and linear evolution equations
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