Clark measures and a theorem of Ritt

  • Isabelle Chalendar
  • Pamela Gorkin
  • Jonathan R. Partington
  • William T. Ross

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.

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Published
2018-04-08
How to Cite
Chalendar, I., Gorkin, P., Partington, J., & Ross, W. (2018). Clark measures and a theorem of Ritt. MATHEMATICA SCANDINAVICA, 122(2), 277-298. https://doi.org/10.7146/math.scand.a-104444
Section
Articles