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Mat. Sb. (N.S.), 1980, Volume 113(155), Number 1(9), Pages 133–145 (Mi msb2782)  

This article is cited in 6 scientific papers (total in 6 papers)

Finiteness of the number of lacunae in the spectrum of the multidimensional polyharmonic operator with a periodic potential

M. M. Skriganov


Abstract: The spectrum of the multidimensional polyharmonic differential operator is investigated. The finiteness of the number of connected components of the spectrum is proved.
Bibliography: 10 titles.

Full text: PDF file (575 kB)
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English version:
Mathematics of the USSR-Sbornik, 1982, 41:1, 115–125

Bibliographic databases:

UDC: 517.9
MSC: 31B30, 35J30, 35P05, 47E05
Received: 26.11.1979

Citation: M. M. Skriganov, “Finiteness of the number of lacunae in the spectrum of the multidimensional polyharmonic operator with a periodic potential”, Mat. Sb. (N.S.), 113(155):1(9) (1980), 133–145; Math. USSR-Sb., 41:1 (1982), 115–125

Citation in format AMSBIB
\Bibitem{Skr80}
\by M.~M.~Skriganov
\paper Finiteness of the number of lacunae in the spectrum of the multidimensional polyharmonic operator with a~periodic potential
\jour Mat. Sb. (N.S.)
\yr 1980
\vol 113(155)
\issue 1(9)
\pages 133--145
\mathnet{http://mi.mathnet.ru/msb2782}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=590542}
\zmath{https://zbmath.org/?q=an:0479.35068|0464.35064}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 41
\issue 1
\pages 115--125
\crossref{https://doi.org/10.1070/SM1982v041n01ABEH002224}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. M. Skriganov, “Spectrum of multidimensional operators with periodic coefficients”, Funct. Anal. Appl., 16:4 (1982), 319–321  mathnet  crossref  mathscinet  zmath  isi
    2. Skriganov M., “The Spectrum Structure of the Multidimensional Schrodinger Operator with a Periodic Potential”, 262, no. 4, 1982, 847–850  mathscinet  isi
    3. M. M. Skriganov, “The multidimensional Schrödinger operator with a periodic potential”, Math. USSR-Izv., 22:3 (1984), 619–645  mathnet  crossref  mathscinet  zmath
    4. O. A. Veliev, “Asymptotic formulas for the eigenvalues of a periodic Schrödinger operator and the Bethe–Sommerfeld conjecture”, Funct. Anal. Appl., 21:2 (1987), 87–100  mathnet  crossref  mathscinet  zmath  isi
    5. Yu. E. Karpeshina, “Analytic perturbation theory for a periodic potential”, Math. USSR-Izv., 34:1 (1990), 43–64  mathnet  crossref  mathscinet  zmath
    6. Elton D., “The Bethe-Sommerfeld Conjecture for the 3-Dimensional Periodic Landau Operator”, Rev. Math. Phys., 16:10 (2004), 1259–1290  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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