On a functional equation related to an automorphism of a unit circle

Abstract

In this article the complete description of the decisions of a functional equation f(w(z))=f(w(0))f(z) is given, where w(z)- automorphism of a unit circle E and the decisions are searched among analytical in E functions. It is established, that research of a given functional equation is closely connected to property of stationary points of automorphism w(z).