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On the discrete spectrum of a perturbed periodic Schrödinger operator. (English. Russian original) Zbl 0825.47014

J. Math. Sci., New York 71, No. 1, 2269-2272 (1994); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 190, 157-162 (1991).

MSC:

47F05 General theory of partial differential operators
47A40 Scattering theory of linear operators
47A10 Spectrum, resolvent
35J10 Schrödinger operator, Schrödinger equation
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References:

[1] M. Sh. Birman, ”The discrete spectrum in a gap of the perturbed operator at large coupling constants,” in: Proceedings of the Conference: Rigorous Results in Quantum Dynamics (1990) (in press).
[2] I. M. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators, Israel Program for Scientific Translations, Jerusalem (1965). · Zbl 0143.36505
[3] M. Sh. Birman, ”On the spectrum of singular boundary problems,” Mat. Sb.,55 (97), 125–174 (1961).
[4] M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV. Analysis of Operators, Academic Press, New York (1978). · Zbl 0401.47001
[5] F. S. Rofe-Beketov, ”Spectrum perturbations, the Kneser-type constants and the effective masses of zone-type potentials,” in: Constructive Theory of Functions’ 84, Sofia (1984), pp. 757–766.
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