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When do finite Blaschke products commute?

Published online by Cambridge University Press:  17 April 2009

Isabelle Chalendar  and
Raymond Mortini
Isabelle Chalendar
Affiliation:
Institut Girard Desargues, UFR de Mathématiques, Université Lyon 1, 69622 Villeurbanne Cedex, France, e-mail: chalenda@desargues.univ-lyonl.fr
Raymond Mortini
Affiliation:
Université de Metz, Département de Mathématiques, Ile de Saulcy, F-57045 Metz, France, e-mail: mortini@poncelet.sciences.univ-metz.fr
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We study the following questions. Which finite Blaschke products are eigenvectors of the composition operators Tu: f ↦ f ∘ u, what are the possible eigenvalues, and which pairs (B, C) of finite Blaschke products commute (that is, satisfy B ∘ C = C ∘ B).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 189 - 200
Copyright
Copyright © Australian Mathematical Society 2001

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