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PSEUDOCONTINUATION AND CYCLICITY FOR RANDOM POWER SERIES

Published online by Cambridge University Press:  27 February 2008

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)

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.

Type
Research Article
Copyright
2008 Cambridge University Press

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