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Cyclicity and invariant subspaces in the Dirichlet spaces
Language
en
Article de revue
This item was published in
Journal Functional Analysis. 2016-02-02, vol. 270, n° 9, p. 3262-3279
English Abstract
Let $\mu$ be a positive finite measure on the unit circle and $\mathcal{D} (\mu)$ the associated Dirichlet space. The generalized Brown-Shields conjecture asserts that an outer function $f \in \mathcal{D} (\mu )$ is ...Read more >
Let $\mu$ be a positive finite measure on the unit circle and $\mathcal{D} (\mu)$ the associated Dirichlet space. The generalized Brown-Shields conjecture asserts that an outer function $f \in \mathcal{D} (\mu )$ is cyclic if and only if $c_\mu (Z (f))= 0$, where $c_\mu$ is the capacity associated with $\mathcal{D} (\mu)$ and $Z(f)$ is the zero set of $f$. In this paper we prove that this conjecture is true for measures with countable support. We also give in this case a complete and explicit characterization of invariant subspaces.Read less <
Origin
Hal imported