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arXiv · 0704.2789

Pseudocontinuation and cyclicity for random power series

Evgeny Abakumov·Alexei Poltoratski
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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.

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Evgeny Abakumov, Alexei Poltoratski. 2007-04-20. Pseudocontinuation and cyclicity for random power series. https://arxiv.org/abs/0704.2789

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