A New Parametrization of Rational Inner Functions of Fixed Degree: Schur Parameters and Realizations

Abstract.

We present a new parametrization of inner functions based on the Schur algorithm. We make use of state space formulas (in practice we obtain a new parametrization of observable pairs). The main advantage of our parametrization is that for each chart the observability gramian is constant: this leads to very good behavior in some approximation problems.