Nevanlinna-pick Interpolation: the Degenerated Case
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Solution of a multiple Nevanlinna-Pick problem for Schur functions via orthogonal rational functions
An interpolation problem of Nevanlinna-Pick type for complexvalued Schur functions in the open unit disk is considered. We prescribe the values of the function and its derivatives up to a certain order at finitely many points. Primarily, we study the case that there exist many Schur functions fulfilling the required conditions. For this situation, an application of the theory of orthogonal rati...
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We give an elementary proof of Sarason’s solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The proofs are based on a reduction method due to Nevanlinna and the fact that reduction of functions corresponds to Schur complementation of the corresponding Pick...
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