Skip to main content
Log in

On discreteness of the spectrum of some operator sheaves associated with a periodic Schrödinger equation

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

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.

Literature Cited

  1. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Academic Press, New York (1978).

    Google Scholar 

  2. N. Ashcroft and N. Mermin, Solid-State Physics, Vol. 1 [Russian translation], Mir, Moscow (1979).

    Google Scholar 

  3. F. Odeh and J. B. Keller, J. Math. Phys.,5, 1499 (1964).

    Google Scholar 

  4. L. E. Thomas, Commun. Math. Phys.,46, 153 (1973).

    Google Scholar 

  5. J. Avron and B. Simon, Ann. Phys. (N.Y.),110, 85 (1977).

    Google Scholar 

  6. V. V. Dyakin and S. I. Petrukhnovskii, Dokl. Akad. Nauk SSSR,264, 1117 (1982).

    Google Scholar 

  7. P. S. Aleksandrov and B. A. Pasynkov, Introduction to the Theory of Dimension [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  8. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin (1966); (Russian translation published by Mir, Moscow (1972)).

    Google Scholar 

  9. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonself-Adjoint Operators, AMS, Providence, R.I. (1969).

    Google Scholar 

  10. B. M. Levitan, Almost Periodic Functions [in Russian], Gostekhteorizdat, Moscow (1953).

    Google Scholar 

  11. G. Veil', “On the uniform distribution of numbers modulo one,” in: Selected Works [Russian translations], Nauka, Moscow (1984), p. 58.

    Google Scholar 

  12. A. G. Kurosh, A Course of Higher Algebra [in Russian], Nauka, Moscow (1971).

    Google Scholar 

Download references

Authors

Additional information

Institute of Metal Physics, Ural Scientific Center of the USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 74, No. 1, pp. 94–102, January, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dyakin, V.V., Petrukhnovskii, S.I. On discreteness of the spectrum of some operator sheaves associated with a periodic Schrödinger equation. Theor Math Phys 74, 66–72 (1988). https://doi.org/10.1007/BF01018212

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01018212

Navigation