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Boundary Nevanlinna–Pick interpolation via reduction and augmentation

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An Erratum to this article was published on 20 January 2011

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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Authors and Affiliations

  1. Department of Mathematics, University of California at San Diego, La Jolla, CA, 92103, USA

    Jim Agler

  2. School of Mathematics, Leeds University, Leeds, LS2 9JT, UK

    N. J. Young

Authors
  1. Jim Agler
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  2. N. J. Young
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Correspondence to N. J. Young.

Additional information

J. Agler is partially supported by National Science Foundation Grant DMS 0801259 and N. J. Young is supported by EPSRC Grant EP/G000018/1.

An erratum to this article can be found at http://dx.doi.org/10.1007/s00209-010-0839-6

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Agler, J., Young, N.J. Boundary Nevanlinna–Pick interpolation via reduction and augmentation. Math. Z. 268, 791–817 (2011). https://doi.org/10.1007/s00209-010-0696-3

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