Skip to main content
Log in

Spectral theory of a class of canonical differential systems

  • Published:
Functional Analysis and Its Applications Aims and scope

Abstract

The general spectral theory of canonical systems is used to study a generalized Krein system. Direct and inverse problems for this system are considered. In particular, some proofs are supplied for Krein's results published by him without proof.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. G. Krein, “Continual analogs of propositions on orthogonal polynomials on the unit circle,” Dokl. Akad. Nauk SSSR,105, No. 4, 637–640 (1955).

    MATH  MathSciNet  Google Scholar 

  2. L. A. Sakhnovich, “On one class of canonical systems on half-axis,” Integral Equations Operator Theory,31, No. 1, 92–112 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  3. L. A. Sakhnovich, Spectral Theory of Canonical Differential Systems. Method of Operator Identities, Operator Theory. Advances and Applications, vol. 107. Birkhäuser, 1999.

  4. V. P. Potapov, “The multiplicative structure ofj-contractive matrix functions,” Amer. Math. Soc. Transl., 15, 131–243 (1960).

    MATH  MathSciNet  Google Scholar 

  5. B. M. Levitan, Inverse Sturm-Liouville Problems, VNU Science Press, 1987.

  6. I. I. Privalov, The Boundary Properties of Analytic Functions [in Russian], Gosizdat, 1950.

  7. Yu. A. Rozanov, Stationary Random Processes, Holden-Day, Amsterdam, 1967.

    MATH  Google Scholar 

  8. Yu. P. Ginzburg, “Multiplicative representation of operator functions of bounded type,” Usp. Math. Nauk,22, No. 1, 163–165 (1967).

    MathSciNet  Google Scholar 

  9. Yu. P. Ginzburg and L. V. Shevchuk, “On the Potapov theory of multiplicative representations,” In: Operator Theory, Advances and Applications, vol. 72, birkhäuser, 1994, pp. 28–47.

  10. L. A. Sakhnovich, “Dissipative operators with absolutely continuous spectrum,” Trudy Mosk. Mat. Obshch.,19, 211–270, (1968).

    MATH  Google Scholar 

Download references

Authors

Additional information

Academy of Radio and Communication, Department of Mathematics, Odessa, Ukraine. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 34, No. 2, pp. 50–62, April–June, 2000.

Translated by L. A. Sakhnovich

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sakhnovich, L.A. Spectral theory of a class of canonical differential systems. Funct Anal Its Appl 34, 119–128 (2000). https://doi.org/10.1007/BF02482425

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02482425

Keywords

Navigation