DOI
10.7146/math.scand.a-104444
Abstract
We determine when a finite Blaschke product B can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt's problem) in terms of the Clark measure for B. Our tools involve the numerical range of compressed shift operators and the geometry of certain polygons circumscribing the numerical range of the relevant operator. As a consequence of our results, we can determine, in terms of Clark measures, when two finite Blaschke products commute.
Document Type
Article
Publication Date
4-8-2018
Publisher Statement
Copyright © 2018, MATHEMATICA SCANDINAVICA.
DOI: https://doi.org/10.7146/math.scand.a-104444.
The definitive version is available at: https://www.mscand.dk/article/view/104444.
Recommended Citation
Chalendar, I., Gorkin, P., Partington, J. R., & Ross, W. T. "Clark measures and a theorem of Ritt." MATHEMATICA SCANDINAVICA, 122, 2 (2018), 277–298. https://doi.org/10.7146/math.scand.a-104444