Infinitesimal generators of invertible evolution families

Abstract

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.

Methods Funct. Anal. Topology, accepted; ver.4 (v4) is the accepted version

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• Recurrence formula for some higher order evolution equations