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Methods Funct. Anal. Topology 23 (2017), no. 1, 26–36
A logarithm representation of operators is introduced as well as a concept of pre-infinitesimal generator. Generators of invertible evolution families are represented by the logarithm representation, and a set of operators represented by the logarithm is shown to be associated with analytic semigroups. Consequently generally-unbounded infinitesimal generators of invertible evolution families are characterized by a convergent power series representation.