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.
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Literature cited
I. M. Vinogradov, Selected Works [in Russian], Moscow (1952), pp. 3–28.
M. M. Skriganov, “Proof of the Bethe-Sommerfeld conjecture in dimension two,” Dokl. Akad. Nauk SSSR,248, No. 1, 39–42 (1979).
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).
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).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 109, pp. 131–133, 1981.
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Popov, V.N., Skriganov, M.M. Remark on the spectrum structure of the two-dimensional Schrödinger operator with the periodic potential. J Math Sci 24, 239–240 (1984). https://doi.org/10.1007/BF01087244
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DOI: https://doi.org/10.1007/BF01087244