Abstract
We consider a general matrix version of a Pick-Loewner interpolation problem on the closed unit disk. Solutions are allowed to have a finite numberl of free poles in the open disk. We show that the smallestl for which a solution to the problem exists is the number of negative eigenvalues of an appropriately defined “Pick matrix,” and for this value ofl we obtain a linear fractional map parametrization of the class of all solutions. The idea is to adapt the Grassmannian approach involving Krein space geometry and invariant subspace representations of the authors; this was successful previously for the case where all interpolating points are inside the disk. Also an appendix includes an errata to earlier work together with simplified proofs.
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Research was supported in part by the National Science Foundation.
Research was supported in part by the National Science Foundation, Office of Naval Research and the Air Force Office of Scientific Research.
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Ball, J.A., Helton, J.W. Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions. Integr equ oper theory 9, 155–203 (1986). https://doi.org/10.1007/BF01195006
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DOI: https://doi.org/10.1007/BF01195006