Interpolation problems of PickNevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions
 Joseph A. Ball,
 J. William Helton
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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.
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 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
 19860301
 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