Title

Decomposing Finite Blaschke Products

Publication Date

Winter 1-2015

Journal

Journal of Mathematical Analysis and its Applications

Volume

426

Issue

2

First Page

1201

Last Page

1216

Abstract

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.

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