Boundary Nevanlinna-Pick interpolation via reduction and augmentation
Jim Agler, N. J. Young
TL;DR
This paper provides an elementary proof and a concrete parametrization of solutions for boundary Nevanlinna-Pick interpolation problems, utilizing reduction methods related to Schur complementation of Pick matrices.
Contribution
It offers a new elementary proof of Sarason's solvability criterion and explicitly characterizes all solutions for boundary interpolation problems.
Findings
Elementary proof of Sarason's criterion
Concrete parametrization of solutions
Connection between reduction and Schur complementation
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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