On the wandering property in Dirichlet spaces
2019
We show that in a scale of weighted Dirichlet spaces $D_{\alpha}$, including the Bergman space, given any finite Blaschke product $B$ there exists an equivalent norm in $D_{\alpha}$ 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 $|\alpha| \leq \frac{\log (2)}{\log(k+1)}$, the chosen norm is the usual one in $D_\alpha$.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
15
References
0
Citations
NaN
KQI