Characteristic Functions and Colligations

The characteristic function of row contractions and the characteristic function of liftings of row contractions are multi-analytic operators which are complete invariants up to unitary equivalence for row contractions and liftings of row contractions, respectively. We provide alternate proofs for these properties of characteristic functions using colligations. Co-isometric observable colligations with certain class of basic operators are characterized. Blaschke factor based transformations of the characteristic function of lifting are studied.