Two-isometries and de Branges-Rovnyak spaces

Karim Kellay (1) , Mohamed Zarrabi (1)

1 IMB - Institut de Mathématiques de Bordeaux

We characterize the symbols of the de Branges--Rovnyak spaces for which the shift operator is concave or two-isometry. As applications, we consider wandering z-invariant subspaces and equality between a de Branges--Rovnyak space and a Dirichlet-type space.

Mots clés: Dirichlet space; de Branges-Rovnyak space; two-isometry

Domaines: Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]; Analyse classique [math.CA]

Karim Kellay, Mohamed Zarrabi. Two-isometries and de Branges-Rovnyak spaces. 2014. ⟨hal-00962422v1⟩