We arrive at the de Branges-Rovnyak space D (W) from the point of view of model theory, ie,
as the space associated with a canonical model for a general completely nonunitary
contraction operator on a Hilbert space. Connections with systems theory make contact with
the approach of Livsic and Brodskii, in particular, the role of the characteristic function as the
transfer function of a unitary system. The connection between invariant subspaces and
regular factorizations leads to the introduction of the overlapping spaces of de Branges …