  The logarithmic representation of infinitesimal generators is generalized to
the cases when the evolution operator is unbounded. The generalized result is
applicable to the representation of infinitesimal generators of unbounded
evolution operators, where unboundedness of evolution operator is an essential
ingredient of nonlinear analysis. In conclusion a general framework for the
identification between the infinitesimal generators with evolution operators is
established. A mathematical framework for such an identification is
indispensable to the rigorous treatment of nonlinear transforms: e.g.,
transforms appearing in the theory of integrable systems.
