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Parameterization of Intertwining Liftings and its Applications

  • C. Foias
  • A. E. Frazho
  • I. Gohberg
  • M. A. Kaashoek
Part of the Operator Theory Advances and Applications book series (OT, volume 100)

Abstract

In this chapter it is shown that the set of all intertwining liftings with tolerance γ in the commutant lifting theorem is parameterized by a natural set of contractive analytic operator-valued functions. A Redheffer scattering interpolation of this parameterization is given. In the final three sections, state space formulas are given for the Redheffer scattering matrix parameterizing the set of all solutions for the standard left Nevanlinna-Pick, Nehari and two-block interpolation problems.

Keywords

Interpolation Problem Open Unit Disc Unilateral Shift Pointwise Stable Mobius Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • C. Foias
    • 1
  • A. E. Frazho
    • 2
  • I. Gohberg
    • 3
  • M. A. Kaashoek
    • 4
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Department of AeronauticsPurdue UniversityWest LafayetteUSA
  3. 3.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael
  4. 4.Dept. of Mathematics and Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands

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