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PSEUDOCONTINUATION AND CYCLICITY FOR RANDOM POWER SERIES

Published online by Cambridge University Press:  27 February 2008

Evgeny Abakumov  and
Alexei Poltoratski
Evgeny Abakumov
Affiliation:
Université Paris-Est, Laboratoire d'Analyse et de Mathematiques Appliquées, UMR CNRS 8050, 5 Bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France (evgueni.abakoumov@univ-mlv.fr)
Alexei Poltoratski
Affiliation:
Texas A&M University, Department of Mathematics, College Station, TX 77843, USA (alexeip@math.tamu.edu)
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Abstract

We prove that a random function in the Hardy space $H^2$ is a non-cyclic vector for the backward shift operator almost surely. The question of existence of a local pseudocontinuation for a random analytic function is also studied.

Keywords

random seriespseudocontinuationcyclic vectorsbackward shiftPrimary 30B2047B37
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 7 , Issue 3 , July 2008 , pp. 413 - 424
Copyright
2008 Cambridge University Press

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