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Pseudocontinuation and cyclicity for random power series

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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693066
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Submitted on : Tuesday, May 1, 2012 - 7:53:46 PM
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Evgeny Abakumov, Alexei Poltoratski. Pseudocontinuation and cyclicity for random power series. Journal of the Institute of Mathematics of Jussieu, Cambridge University Press (CUP), 2008, 7 (3), pp.413--424. ⟨10.1017/S1474748008000121⟩. ⟨hal-00693066⟩

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