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Canonical Systems on the Line with Rational Spectral Densities: Explicit Formulas

  • I. Gohberg
  • M. A. Kaashoek
  • A. L. Sakhnovich
Part of the Operator Theory: Advances and Applications book series (OT, volume 117)

Abstract

Explicit formulas for the direct and inverse spectral problems for a canonical system on the full line with rational spectral density are obtained via a reduction to the half line case.

AMS Classification Primary

34L05 34A55 34A05 34B20 47N20 

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References

  1. [1]
    D. Alpay and I. Gohberg, Inverse spectral problem for differential operators with rational scattering matrix functions,J. Diff. Eq. 118 (1995), 1–19.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    I. Gohberg, M.A. Kaashoek and A L Sakhnovich, Canonical systems with rational spectral densities: explicit formulas and applications, Math. Nachr. 194 (1998), 93–125.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    P. Lancaster and L. Rodman, Algebraic Riccati equations, Clarendon Press, Oxford, 1995.zbMATHGoogle Scholar
  4. [4]
    B.M. Levitan, Inverse Sturm-Liouville problems, VSP, Zeist, 1987.zbMATHGoogle Scholar
  5. [5]
    B.M. Levitan and I.S. Sargsjan, Sturm-Liouville systems and Dirac operators, Mathematics and its Applications, vol. 69 Kluwer Academic, Dordrecht, 1991.Google Scholar
  6. [6]
    F.E. Melik-Adamjan, Canonical differential operators in a Hilbert space, Izv. Akad. Nauk Arm. SSR Math. 12 (1977), 10–31 (Russian).MathSciNetGoogle Scholar
  7. [7]
    L. Roozemond, Canonical pseudo-spectral factorization and Wiener-Hopf integral equations, in: Constructive methods of Wiener-Hopf factorization (eds. I. Gohberg and M.A. Kaashoek), OT 21, Birkhäuser Verlag, Basel, 1986, pp. 127–156.CrossRefGoogle Scholar
  8. [8]
    L.A. Sakhnovich, Spectral theory of canonical differential systems, method of operator identities, OT, Birkhauser Verlag, to appear.Google Scholar

Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • I. Gohberg
    • 1
  • M. A. Kaashoek
    • 2
  • A. L. Sakhnovich
    • 3
  1. 1.School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael
  2. 2.Faculteit der Exacte WetenschappenVrije UniversiteitAmsterdamThe Netherlands
  3. 3.Branch of Hydroacoustics, Marine Institute of HydrophysicsNASU Preobradzenskaya 3OdessaUkraine

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