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The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential

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References

  1. Bolle, U.: Dichteabschätzungen für mehrfache gitterförmige Kudelanordnungen im ℝm. Studia Sci. Math. Hungarica14, (N 1-3), 51–68 (1979)

    Google Scholar 

  2. Callaway, J.: Energy hand theory. New York: Academic Press 1964

    Google Scholar 

  3. Cassels, J.W.S.: An introduction to the geometry of numbers. Berlin-Göttingen-Heidelberg: Springer 1959

    Google Scholar 

  4. Dahlberg, B.E.J., Trubowitz, E.: A remark on two dimensional periodic potentials. Comment. Math. Helvetici57, (N 1), 130–134 (1982)

    Google Scholar 

  5. Eastham, M.S.P.: The spectral theory of periodic differential equations. Edinburgh: Scottish Academic Press 1973

    Google Scholar 

  6. Landau, E.: Vorlesungen über Zahlentheorie. Bd. 2. Leipzig: Hirzel 1927

    Google Scholar 

  7. Popov, V.N., Skriganov, M.M.: A remark on the spectrum structure of the two dimensional Schrödinger operator with periodic potential. Notes Sci. Sem. Steklov Math. Inst. (Leningrad Branch)109, 131–133 (1981)

    Google Scholar 

  8. Reed, M., Simon, B.: Methods in modern mathematical physics. Vol. IV: Analysis of operators. New York: Academic Press 1978

    Google Scholar 

  9. Skriganov, M.M.: Prof of the Bethe-Sommerfeld hypothesis in dimension two. Dokl. Akad. Nauk SSSR248 (N 1), 39–42 (1979)

    Google Scholar 

  10. Skriganov, M.M.: General properties of the spectrum of differential and pseudodifferential operators with periodic coefficients and some problems of the geometry of numbers. Dokl. Akad. Nauk SSSR256 (N 1), 47–51 (1981)

    Google Scholar 

  11. Skriganov, M.M.: On the spectrum of the multi-dimensional operators with periodic coefficients. Func. Anal. i Pril.16 (N 4), 88–89 (1982)

    Google Scholar 

  12. Skriganov, M.M.: The multi-dimensional Schrödinger operator with periodic potential. Izvestiya Akad. Nauk SSSR (Ser. Math.)47, (N 3), 659–687 (1983)

    Google Scholar 

  13. Skriganov, M.M.: Geometrical and arithmetical methods in the spectral theory of the multidimensional periodic operators. Proc. Steklov Math. Inst. Vol. 171. Moscow-Leningrad: Nauka 1984 (to appear)

    Google Scholar 

  14. Skriganov, M.M.: Proof of the Bethe-Sommerfeld hypothesis in dimension three. LOMI Preprints: P-6-84 (1984)

  15. Sommerfeld, A., Bethe, H.: Elektronentheorie der Metalle. Handbuch der Physik. 2nd. ed. Bd. XXIV/2. Berlin: Springer 1933

    Google Scholar 

  16. Yakovlev, N.N.: Asymptotic estimates of the density of latticek-packing andk-covering and the spectrum structure of the Schrödinger operator with periodic potential. Doklady Akad. Nauk SSSR276 (N 1), 54–57 (1984)

    Google Scholar 

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Skriganov, M.M. The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential. Invent Math 80, 107–121 (1985). https://doi.org/10.1007/BF01388550

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