On the wandering property in Dirichlet spaces

2019/04/05 by Gallardo-Gutiérrez, Eva, Partington, Jonathan, Seco, Daniel
#47B38 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.02974

Abstract

We show that in a scale of weighted Dirichlet spaces D_α, including the Bergman space, given any finite Blaschke product B there exists an equivalent norm in D_α such that B satisfies the wandering subspace property with respect to such norm. This extends, in some sense, previous results by Carswell, Duren and Stessin. As a particular instance, when B(z)=z^k and |α| ≤ (log (2))/(log(k+1)), the chosen norm is the usual one in D_α.

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