Skip to main content
Log in

On Higher Regularized Traces of a Differential Operator with Bounded Operator Coefficient Given in a Finite Interval

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this work, we find a higher regularized trace formula for a regular Sturm–Liouville differential operator with operator coefficient.

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. Adıgüzelov, E.E.: About the trace of the difference of two Sturm–Liouville operators with operator coefficient, iz.An Az SSR, seriya fiz-tekn. i mat.nauk, 5, 20–24 (1976)

  2. Adıgüzelov, E.E., Avcı, H., Gül, E.: The trace formula for Sturm–Liouville operator with operator coefficient. J. Math. Phys. 42(6), 1611–1624 (2001)

    Article  MathSciNet  Google Scholar 

  3. Adıgüzelov, E.E., Bakṣi, O.: On the regularized traced of the differential operator equation given in a finite interval. J. Eng. Nat. Sci. Sigma 47–55 (2004/1)

  4. Adıgüzelov, E.E., Sezer, Y.: The second regualrized trace of ASelf adjoint differential operator given in a finite interval with bounded operator coefficient. Math. Comput. Model. 53, 553–565 (2011)

    Article  Google Scholar 

  5. Cohberg, C., Krein, M.G.: Introduction to the Theory Linear Non-self Adjoint Operators, Translation of Mathematical Monographs, vol. 18. AMS, Providence (1969)

    Google Scholar 

  6. Dikiy, L.A.: About a formula of Gelfand–Levitan. Usp. Mat. Nauk. 8(2), 119–123 (1953)

    Google Scholar 

  7. Dikiy, L.A.: The zeta function of an ordinary differential equation on a finite interval. IZV. Akad. Nauk. SSSR 19(4), 187–200 (1955)

    MathSciNet  Google Scholar 

  8. El Raheem, Z.F.A., Nassef, A.H.: The regularized trace formula of the spectrum of a Dirichlet boundary problem with turning point. Abstr. Appl. Anal. 2012, 492576 (2012)

    MathSciNet  MATH  Google Scholar 

  9. Faddeev, L.D.: On the expression for the trace of the difference of two singular differential operators of the Sturm Liouville type. Dokl. Akad. Nauk. SSSR 115(5), 878–881 (1957)

    MathSciNet  MATH  Google Scholar 

  10. Fulton, T.C., Pruess, S.A.: Eigenvalue and eigenfunction asymptotics for regular Sturm–Liouville problems. J. Math. Anal. Appl. 188, 297–340 (1994)

    Article  MathSciNet  Google Scholar 

  11. Gasymov, M.G.: On the sum of differences of eigenvalues of two self adjoint operators. Dokl. Akad. Nauk. SSSR 150(6), 1202–1205 (1963)

    MathSciNet  Google Scholar 

  12. Gelfand, I.M.: On the identities for eigenvalues of differential operator of second order. Usp. Mat. Nauk. (N.S.) 11(1), 191–198 (1956)

    MathSciNet  Google Scholar 

  13. Gelfand, I.M., Levitan, B.M.: On a formula for eigenvalues of a differential operator of second order. Dokl. Akad. Nauk. SSSR 88(4), 593–596 (1953)

    Google Scholar 

  14. Halilova, R.Z.: On regularization of the trace of the Sturm–Liouville operator equation. Funks.analiz, teoriya funksi i ik pril.-Mahachkala 1(3), 154–161 (1976)

  15. Kirillov, A.A.: Elements of the theory of representations. Springer, New York (1976)

    Book  Google Scholar 

  16. Levitan, B.M.: Calculation of the regularized trace for the Sturm Liouville operator. Usp. Mat. Nauk. 19(1), 161–165 (1964)

    MathSciNet  Google Scholar 

  17. Levitan, B.M., Sargsyan, I.S.: Sturm–Liouville and Dirac Operators. Kluwer, Dordrecht (1991)

    Book  Google Scholar 

  18. Maksudov, F.G., Bayramoglu, M., Adıgüzelov, E.E.: On a regularized traces of the Sturm–Liouville operator on a finite interval with the unbounded operator coefficient. Dokl. Akad. Nauk. SSSR (English translation, Sov. Math. Dokl.) 30(1), 169–173 (1984)

    Google Scholar 

  19. Yang, C.F.: New trace formula for the matrix Sturm–Liouville equation with Eigen parameter dependent boundary condition. Turk. J. Math. 37, 278–285 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Yonca Sezer.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sezer, Y., Bakşi, Ö. & Karayel, S. On Higher Regularized Traces of a Differential Operator with Bounded Operator Coefficient Given in a Finite Interval. Mediterr. J. Math. 18, 90 (2021). https://doi.org/10.1007/s00009-021-01719-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-021-01719-3

Keywords

Mathematics Subject Classification

Navigation