Integral Equations and Operator Theory
, Volume 9, Issue 2, pp 155203
First online:
Interpolation problems of PickNevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions
 Joseph A. BallAffiliated withDepartment of Mathematics, Virginia Polytechnic Institute
 , J. William HeltonAffiliated withDepartment of Mathematics, University of California
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We consider a general matrix version of a PickLoewner 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.
 Title
 Interpolation problems of PickNevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions
 Journal

Integral Equations and Operator Theory
Volume 9, Issue 2 , pp 155203
 Cover Date
 198603
 DOI
 10.1007/BF01195006
 Print ISSN
 0378620X
 Online ISSN
 14208989
 Publisher
 BirkhäuserVerlag
 Additional Links
 Topics
 Authors

 Joseph A. Ball ^{(1)}
 J. William Helton ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Virginia Polytechnic Institute, 24061, Blacksburg, VA, USA
 2. Department of Mathematics, University of California, 92093, San Diego, La Jolla, CA, USA