  Operator representation of Cole-Hopf transform is obtained based on the
logarithmic representation of infinitesimal generators. For this purpose the
relativistic formulation of abstract evolution equation is introduced. Even
independent of the spatial dimension, the Cole-Hopf transform is generalized to
a transform between linear and nonlinear equations defined in Banach spaces. In
conclusion a role of transform between the evolution operator and its
infinitesimal generator is understood in the context of generating nonlinear
semigroup.
