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Cyclicity of singular inner functions from the corona theorem

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

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

1.Beurling, A., A critical topology in harmonic analysis on semigroups, Acta Math. 112 (1964), 215–228.Google Scholar
2.Borichev, A. and Hedenmalm, H., Completeness of translates in weighted spaces on the half-line, Acta Math. 174 (1995), 1–84.Google Scholar
3.Carleson, L., Interpolations by bounded analytic functions and the corona problem, Annals Math. 76 (1962), 547–559.Google Scholar
4.Gevorkyan, I. M. and Shamoyan, F. A., Weak invertibility in spaces of functions, analytic in the disk, which permit growth near its boundary, Akad. Nauk Armyan. SSR Dokl. 82 (1986), 156–159.Google Scholar
5.Keldyš, M. V., Sur l'approximation en moyenne par polynomes des fonctions d'une variable complexe, Mat. Sb. 16(58) (1945), 1–20.Google Scholar
6.Nikolskii, N. K., Selected problems of weighted approximation and analysis, Proceedings of the Steklov Institute of Mathematics, Volume 120 (American Mathematical Society, Providence, RI, 1974).Google Scholar
7.Nikolskii, N. K., Treatise on the shift operator (Springer, 1986).Google Scholar
8.Roberts, J. W., Cyclic inner functions in the Bergman spaces and weak outer functions in Hp, 0 < p < 1, Illinois J. Math. 29 (1985), 25–38.Google Scholar