Skip to main content
SpringerLink
Log in

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

  • Conference paper
Differential Operators and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Alpay and I. Gohberg, Inverse spectral problem for differential operators with rational scattering matrix functions,J. Diff. Eq. 118 (1995), 1–19.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Lancaster and L. Rodman, Algebraic Riccati equations, Clarendon Press, Oxford, 1995.

    MATH  Google Scholar 

  4. B.M. Levitan, Inverse Sturm-Liouville problems, VSP, Zeist, 1987.

    MATH  Google Scholar 

  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. F.E. Melik-Adamjan, Canonical differential operators in a Hilbert space, Izv. Akad. Nauk Arm. SSR Math. 12 (1977), 10–31 (Russian).

    MathSciNet  Google Scholar 

  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.

    Chapter  Google Scholar 

  8. L.A. Sakhnovich, Spectral theory of canonical differential systems, method of operator identities, OT, Birkhauser Verlag, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    I. Gohberg

  2. Faculteit der Exacte Wetenschappen, Vrije Universiteit, De Boelelaan 1081a, Amsterdam, 1081 HV, The Netherlands

    M. A. Kaashoek

  3. Branch of Hydroacoustics, Marine Institute of Hydrophysics, NASU Preobradzenskaya 3, Odessa, 270100, Ukraine

    A. L. Sakhnovich

Authors
  1. I. Gohberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Kaashoek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. L. Sakhnovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, University of Odessa, 270026, Odessa, Ukraine

    V. M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    I. Gohberg

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    M. Gorbachuk  & V. Gorbachuk  & 

  4. Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek

  5. Department of Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10/1411, 1040, Vienna, Austria

    H. Langer

  6. Institute of Mathematics, Economics and Mechanics, Odessa State University, 270057, Dvoryanskaya str. 2, Odessa, Ukraine

    G. Popov

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Basel AG

About this paper

Cite this paper

Gohberg, I., Kaashoek, M.A., Sakhnovich, A.L. (2000). Canonical Systems on the Line with Rational Spectral Densities: Explicit Formulas. In: Adamyan, V.M., et al. Differential Operators and Related Topics. Operator Theory: Advances and Applications, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8403-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8403-7_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9552-1

  • Online ISBN: 978-3-0348-8403-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation