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.

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