Abstract
We study a Nevanlinna-Pick type interpolation problem for matrix-valued generalized Carathéodory functions, where the values of the function and the values of its derivatives up to a certain order are prescribed at finitely many points of the open unit disk. Under the assumption that the generalized Schwarz-Pick-Potapov block matrix, which is associated to the given data, is non-singular we establish a correspondence between the set of solutions of the problem and the set of minimal unitary extensions of a certain isometry in a Pontryagin space, which is one-to-one modulo unitary equivalence.
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Klotz, L., Lasarow, A. (2005). An Operator-theoretic Approach to a Multiple Point Nevanlinna-Pick Problem for Generalized Carathéodory Functions. In: Förster, KH., Jonas, P., Langer, H. (eds) Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems. Operator Theory: Advances and Applications, vol 162. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7453-5_12
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