Journal of Soviet Mathematics

, Volume 24, Issue 2, pp 239–240

Remark on the spectrum structure of the two-dimensional Schrödinger operator with the periodic potential

  • V. N. Popov
  • M. M. Skriganov
Article

Abstract

In the remark it is shown that it is possible to omit arithmetical conditions on the period-lattice of the potential in the Schrödinger operator, which were assumed in the previous works of the second author.

Literature cited

  1. 1.
    I. M. Vinogradov, Selected Works [in Russian], Moscow (1952), pp. 3–28.Google Scholar
  2. 2.
    M. M. Skriganov, “Proof of the Bethe-Sommerfeld conjecture in dimension two,” Dokl. Akad. Nauk SSSR,248, No. 1, 39–42 (1979).Google Scholar
  3. 3.
    M. M. Skriganov, “Spectrum structure of the two-dimensional Schrödinger operator with the periodic potential and some arithmetical properties of two-dimensional lattices,” Mat. Inst. Steklov. Akad. Nauk SSSR,157 (1981).Google Scholar
  4. 4.
    M. M. Skriganov, “General properties of the spectrum of differential operators with periodic coefficients and some problems of number geometry,” Dokl. Akad. Nauk SSSR,256, No. 1, 47–51 (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • V. N. Popov
  • M. M. Skriganov

There are no affiliations available

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