A Naimark Dilation Perspective of Nevanlinna-Pick Interpolation

In this paper a positive real tangential Nevanlinna-Pick interpolation problem with interpolation at operator points is solved. The Naimark dilation theorem together with the state space method from systems theory are used to obtain a parameterization for the set of all solutions. Explicit state space formulas are given for both the singular and non-ingular case. In the proofs the solution of an intermediate isometric extension problem plays an important role.