Decomposing Finite Blaschke Products

Authors

Ulrich Daepp, Bucknell UniversityFollow
Pamela Gorkin, Bucknell UniversityFollow
Andrew ShafferFollow
Benjamin Sokolowsky, SUNY Stony BrookFollow
Karl Voss, Bucknell UniversityFollow

Publication Date

Winter 1-2015

Description

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

Journal of Mathematical Analysis and its Applications

Volume

426

Issue

2

First Page

1201

Last Page

1216

Department

Mathematics

Link to Published Version

http://www.sciencedirect.com/science/article/pii/S0022247X1500058X

DOI

10.1016/j.jmaa.2015.01.039

Recommended Citation

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.