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Introduction

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

Abstract

The theory of interpolation with metric constraints started in the beginning of this century with papers of Carathéodory [1], [2] and Schur [1], [2], and was continued by Nevanlinna [1] and Pick [1], [2], and then later in the fifties by Nehari [1]. At the end of the sixties and in the beginning of the seventies operator theoretical methods for solving these classical function theory interpolation problems were discovered. The most important developments started with the papers Adamjan-Arov-Krein [1], Sarason [1], and Sz.-Nagy-Foias [1], [2]. In particular, in 1967 Sarason [1] encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, Sz.-Nagy-Foias [1], [2] derived a purely geometrical extension of Sarason’s results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries, and this work formed the basis of a new method to deal with metric constrained interpolation problems, which usually is referred to as the commutant lifting approach.

Keywords

Interpolation Problem Commutant Lift State Space Solution Nehari Problem Commutant Lift Theorem 
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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