Nonextreme de Branges-Rovnyak Spaces as Models for Contractions.

The de Branges-Rovnyak spaces are known to provide an alternate functional model for contractions on a Hilbert space, equivalent to the Sz.-Nagy-Foias model. The scalar de Branges-Rovnyak spaces $${\mathcal{H}(b)}$$ have essentially different properties, according to whether the defining function b is or not extreme in the unit ball of H. For b extreme the model space is just $${\mathcal{H}(b)}$$ , while for b nonextreme an additional construction is required. In the present paper we identify the precise class of contractions which have as a model $${\mathcal{H}(b)}$$ with b nonextreme. [ABSTRACT FROM AUTHOR]