Clark measures and a theorem of Ritt

• Isabelle Chalendar ^[1] ; Pamela Gorkin ^[2] ; Jonathan R. Partington ^[3] ; William T. Ross ^[4]
  1. [1] University of Marne la Vallée

     University of Marne la Vallée

     París, Francia

     
  2. [2] Bucknell University

     Bucknell University

     Borough of Lewisburg, Estados Unidos

     
  3. [3] University of Leeds

     University of Leeds

     Reino Unido

     
  4. [4] University of Richmond

     University of Richmond

     Estados Unidos

     

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• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 122, Nº 2, 2018, págs. 277-298
• Idioma: inglés
• DOI: 10.7146/math.scand.a-104444
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.