Skip to main content
Log in

On the Discreteness of the Spectrum of the magnetic Schrödinger operator

  • Brief Communications
  • Published:
Functional Analysis and Its Applications Aims and scope

Abstract

We establish sufficient conditions for the discreteness of the spectrum of the magnetic Schrödinger operator in terms of the Lebesgue measure.

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.

References

  1. H. Leinfelder and C. G. Simader, Math. Z., 176:1 (1981), 1–19.

    Article  MathSciNet  MATH  Google Scholar 

  2. V. Kondratiev, V. Maz’ya, and M. Shubin, Comm. Partial Differential Equations, 29:3–4 (2004), 489–521.

    MathSciNet  MATH  Google Scholar 

  3. V. Kondratiev, V. Maz’ya, and M. Shubin, Comm. Partial Differential Equations, 34:10–12 (2009), 1127–1146.

    Article  MathSciNet  MATH  Google Scholar 

  4. B. Simon, Methods Funct. Anal. Topology, 15:1 (2009), 61–66.

    MathSciNet  MATH  Google Scholar 

  5. B. Simon, Functional Integration and Quantum Physics, Academic Press, New York-London, 1979.

    MATH  Google Scholar 

  6. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow, 1977.

    Google Scholar 

  7. W. Arendt and A. V. Bukhvalov, Forum Math., 6:1 (1994), 111–135.

    MathSciNet  MATH  Google Scholar 

  8. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press, New York-London, 1972.

    Google Scholar 

  9. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2: Fourier Analysis, Self-Adjointness, Academic Press, New York-London, 1975.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. R. Aliev.

Additional information

__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 46, No. 4, pp. 83–85, 2012

Original Russian Text Copyright © by A. R. Aliev and E. H. Eyvazov

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aliev, A.R., Eyvazov, E.H. On the Discreteness of the Spectrum of the magnetic Schrödinger operator. Funct Anal Its Appl 46, 305–307 (2012). https://doi.org/10.1007/s10688-012-0037-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10688-012-0037-x

Key words

Navigation