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Interpolation Problems for Operator-Valued Functions

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

Abstract

This chapter concentrates on the necessary and sufficient conditions for the existence of solutions for classical and modern H interpolation problems. These interpolation problems have their roots deep in classical analysis, and they are introduced here in a sophisticated way for operator valued functions with operator arguments. Included are the Nevanlinna-Pick, Hermite-Fejér, Nehari, Sarason and Nudelman interpolation problems, in their classical and tangential form. Both one sided and two-sided versions are considered. Proofs of the main existence results will be given in the next chapter, based on the commutant lifting theorem.

Keywords

Hilbert Space Toeplitz Operator Interpolation Problem Taylor Coefficient Unilateral Shift 
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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