Decomposing Finite Blaschke Products
We present four algorithms to determine whether or not a Blaschke product is a composition of two non-trivial Blaschke products and, if it is, the algorithms suggest what the composition must be. The initial algorithm is a naive counting argument, the second considers critical values and the counting argument, the third is a geometric argument that exploits the relationship between Blaschke products and curves with the Poncelet property, and it can also be expressed in terms of a group associated with the Blaschke product. The final algorithm looks at inverse images under the Blaschke product. Our algorithms are accompanied by an applet that implements them.
Journal of Mathematical Analysis and its Applications
Daepp, Ulrich; Gorkin, Pamela; Shaffer, Andrew; Sokolowsky, Benjamin; and Voss, Karl. "Decomposing Finite Blaschke Products." Journal of Mathematical Analysis and its Applications (2015) : 1201-1216.