Skip to main content
Log in

The Spectrum and Trace Formula for Bounded Perturbations of Differential Operators

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

Spectrum properties and a method for deriving a regularized trace formula for perturbations of operators with discrete spectra in a separable Hilbert space are studied. A trace formula for a local perturbation of a two-dimensional harmonic oscillator in a strip is obtained based on this method.

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. C. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4: Analysis of Operators (Academic, New York, 1978).

    MATH  Google Scholar 

  2. Z. Yu. Fazullin and Kh. Kh. Murtazin, Sb. Math. 192 (5), 725–761 (2001).

    Article  MathSciNet  Google Scholar 

  3. V. A. Sadovnichii and Z. Yu. Fazullin, Differ. Equations 37 (3), 430–438 (2001).

    Article  MathSciNet  Google Scholar 

  4. V. A. Sadovnichii, Z. Yu. Fazullin, and A. I. Atnagulov, Ufimsk. Mat. Zh. 8 (3), 22–40 (2016).

    Article  Google Scholar 

  5. Kh. Kh. Murtazin and Z. Yu. Fazullin, Dokl. Math. 67 (3), 426–428 (2003).

    Google Scholar 

  6. Kh. Kh. Murtazin and Z. Yu. Fazullin, Differ. Equations 45 (4), 564–579 (2009).

    Article  MathSciNet  Google Scholar 

  7. V. A. Sadovnichii and V. V. Dubrovskii, Dokl. Akad. Nauk SSSR 319 (1), 61–62 (1991).

    Google Scholar 

  8. V. E. Podol’skii, Math. Notes 56, 699–703 (1994).

    Article  MathSciNet  Google Scholar 

  9. E. Korotyaev and A. Pushnitski, Funct. Anal. 217 (1), 221–248 (2004).

    Article  MathSciNet  Google Scholar 

  10. A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics (Nauka, Moscow, 1984) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Sadovnichy.

Additional information

Original Russian Text © V.A. Sadovnichy, Z.Yu. Fazullin, I.G. Nugaeva, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 1.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sadovnichy, V.A., Fazullin, Z.Y. & Nugaeva, I.G. The Spectrum and Trace Formula for Bounded Perturbations of Differential Operators. Dokl. Math. 98, 552–554 (2018). https://doi.org/10.1134/S1064562418070050

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562418070050

Navigation