Finite Blaschke Products and Decomposition

Abstract

Let $B(z)$ be a finite Blaschke product of degree $n$. We consider the problem when a finite Blaschke product can be written as a composition of two nontrivial Blaschke products of lower degree related to the condition $% B\circ M=B$ where $M$ is a M\"{o}bius transformation from the unit disk onto itself.