System theory, operator models and scattering: The time-varying case

Daniel Alpay, Joseph A. Ball, Yossi Peretz

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


It is well known that linear system theory, Lax-Phillips scattering theory, and operator model theory for a contraction operator are all intimately related. A common thread in all three theories is a contractive, analytic, operator-valued function on the unit disk W(z) having a representation of the form W(z) = D + zC(I - zA)-1 B, known, depending on the context, as the transfer function, the scattering function, or the characteristic function. We present the time-varing analogue of this framework. Also included is a time-varying analogue of the Abstract Interpolation Problem of Katsnelson-Kheifets-Yuditskii.

Original languageEnglish
Pages (from-to)245-286
Number of pages42
JournalJournal of Operator Theory
Issue number2
StatePublished - 1 Mar 2002


  • Frequency response function
  • Isometric/coisometric/unitary system
  • Lax-Phillips scattering
  • Realization
  • Time-varying system
  • Transfer function

ASJC Scopus subject areas

  • Algebra and Number Theory


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