Abstract.
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.
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Frazho, A., Kaashoek, M. A Naimark Dilation Perspective of Nevanlinna-Pick Interpolation. Integr. equ. oper. theory 49, 323–378 (2004). https://doi.org/10.1007/s00020-003-1287-z
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DOI: https://doi.org/10.1007/s00020-003-1287-z