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arXiv · 0905.4759

Boundary Nevanlinna-Pick interpolation via reduction and augmentation

Jim Agler·N. J. Young
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Abstract

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 Julia and Nevanlinna. Reduction of functions corresponds to Schur complementation of the corresponding Pick matrices.

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Jim Agler, N. J. Young. 2010-11-08. Boundary Nevanlinna-Pick interpolation via reduction and augmentation. https://doi.org/10.1007/s00209-010-0696-3.

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