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Cyclicity of singular inner functions from the corona theorem

Part of: Spaces and algebras of analytic functions General theory of linear operators

Published online by Cambridge University Press:  31 May 2012

Omar El-Fallah ,
Karim Kellay  and
Kristian Seip
Omar El-Fallah
Affiliation:
Département de Mathématiques, Université Mohamed V, BP 1014 Rabat, Morocco (elfallah@fsr.ac.ma)
Karim Kellay
Affiliation:
Centre de Mathématiques et Informatique (CMI), Laboratoire d'Analyse, Topologie, Probabilités (LATP), Université de Provence, 39, rue F. Joliot-Curie, 13453 Marseille Cedex 13, France (kellay@cmi.univ-mrs.fr)
Kristian Seip
Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway (seip@math.ntnu.no
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Abstract

Carleson's corona theorem is used to obtain two results on cyclicity of singular inner functions in weighted Bergman-type spaces on the unit disk. Our method of proof requires no regularity conditions on the weights.

Keywords

weighted Bergman spacecyclic functionsingular inner functioncorona theorem

MSC classification

Secondary: 30H20: Bergman spaces, Fock spaces 30H80: Corona theorems 47A16: Cyclic vectors, hypercyclic and chaotic operators
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 4 , October 2012 , pp. 815 - 824
Copyright
Copyright © Cambridge University Press 2012

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References

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