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18th International Conference on Operator Theory
June 27 - July 1, 2000
University of the West
Timisoara, Romania

Organizers
Dumitru Gaspar, Traian Ceausu, Aurelian Craciunescu, Aurelian Gheondea, Radu-Nicolae Gologan, Ciprian Pop, Dan Popovici, Nicolae Suciu, Alexandru Terescenco, Dan Timotin, Flavius Turcu

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The group of the continuous invariants of a finite Blaschke product
by
Isabelle Chalendar
Universite Lyon 1
Coauthors: Gilles Cassier

Motivated by an open mapping theorem for Scott Brown set, we study the functions u:T --> T which are continuous and invariant for a finite Blaschke product b, that is, which satisfy b o u=b on T. We prove that the set of such functions is a cyclic group G. For that purpose we localize the zeros of the derivative of a Blaschke product (not necessarily finite) and we prove that each element of G has an analytic extension in a corona including T. Finally we study the finite Blaschke products b which have invariants in the disc algebra.

Date received: June 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeo-65.