Integral Equations and Operator Theory

, Volume 9, Issue 2, pp 155–203

Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions

  • Joseph A. Ball
  • J. William Helton

DOI: 10.1007/BF01195006

Cite this article as:
Ball, J.A. & Helton, J.W. Integr equ oper theory (1986) 9: 155. doi:10.1007/BF01195006


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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Copyright information

© Birkhäuser Verlag 1986

Authors and Affiliations

  • Joseph A. Ball
    • 1
  • J. William Helton
    • 2
  1. 1.Department of MathematicsVirginia Polytechnic InstituteBlacksburgUSA
  2. 2.Department of MathematicsUniversity of CaliforniaSan Diego, La JollaUSA

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