Boundary Nevanlinna-Pick interpolation via reduction and augmentation
arXiv:0905.4759 · doi:10.1007/s00209-010-0696-3.
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.
arXiv commentWe have repaired an inaccuracy in the proof of Proposition 6.7, (1) implies (5)