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Reduction Techniques: From Nonstationary to Stationary and Vice Versa

  • 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 presents the reduction technique that will allow us to convert nonstationary interpolation problems into stationary ones. This technique is based on a transformation (and its inverse) which maps a doubly infinite operator matrix \(F{\text{ = }}\left( {{f_{j,k}}} \right)_{j,k{\text{ = - }}\infty }^\infty \) into a doubly infinite block Laurent matrix \(\hat F = \left( {\left[ F \right]_{j - k} } \right)_{j,k = - \infty }^\infty \) where [F]n is the matrix which one obtains from F if all (operator) entries in F are set to zero except those on the n-th diagonal which are left unchanged.

Keywords

Unitary Operator Reduction Technique Toeplitz Operator Bounded Linear Operator Operator Matrix 
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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