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arxiv: 0704.2789 · v1 · submitted 2007-04-20 · 🧮 math.CV

Pseudocontinuation and cyclicity for random power series

classification 🧮 math.CV
keywords randomfunctionpseudocontinuationalmostanalyticbackwardcyclicityexistence
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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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