Decomposing Finite Blaschke Products
Journal of Mathematical Analysis and its Applications
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.
Gorkin, Pamela; Daepp, Ulrich 5237980; Voss, Karl; Shaffer, Andrew; and Sokolowsky, Benjamin. "Decomposing Finite Blaschke Products." Journal of Mathematical Analysis and its Applications 426, no. 2 (2015) : 1201-1216.