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Notes on Interpolation in the Generalized Schur Class. I. Applications of Realization Theory

  • D. Alpay
  • T. Constantinescu
  • A. Dijksma
  • J. Rovnyak
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 134)

Abstract

Realization theory is used to study Nevanlinna-Pick and Carathéo­dory-Fejér interpolation problems for generalized Schur classes. In the first part of the paper, conditions are given for the existence of a solution of a factorization problem that includes Nevanlinna-Pick interpolation and factor­ization problems of Leech type for operator-valued functions. In the second part, an analysis is made of the numbers of positive and negative eigenvalues of classical matrices which arise in coefficient problems. The complete solution of an indefinite Carathéodory-Fejér problem is obtained.

Keywords

Hilbert Space Negative Eigenvalue Interpolation Problem Selfadjoint Operator Partial Isometry 
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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • D. Alpay
    • 1
  • T. Constantinescu
    • 2
  • A. Dijksma
    • 3
  • J. Rovnyak
    • 4
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Programs in Mathematical SciencesUniversity of Texas at DallasRichardsonUSA
  3. 3.Department of MathematicsUniversity of GroningenGroningenThe Netherlands
  4. 4.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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