This paper contains a detailed treatment of the Nevanlinna–Pick interpolation problem for matrix-valued functions. A close relationship with the trigonometric moment problem is put into light. Matrix extensions of Pick’s solvability criterion and Nevanlinna’s iterative algorithm are presented. Necessary and sufficient conditions are obtained for uniqueness of the solution of the infinite interpolation problem. The approach is essentially based upon the theories of J-contractive transformations and of Weyl matrix circles.
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Delsarte et al. (1979) studied this question.
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