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Asymptotic distribution of eigenvalues in a lacuna of the continuous spectrum of the perturbed Hill operator. (English. Russian original) Zbl 0357.34020

Math. Notes 20(1976), 750-755 (1977); translation from Mat. Zametki 20, 341-350 (1976).

MSC:

34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34L99 Ordinary differential operators
47E05 General theory of ordinary differential operators
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References:

[1] I. M. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators, Fizmatgiz, Moscow (1963). · Zbl 0143.36505
[2] F. S. Rofe-Beketov, ?A criterion for the finiteness of the number of discrete levels in a lacuna of the continuous spectrum caused by a perturbation of the periodic potential,? Dokl. AN SSSR,156, No. 3, 515?518 (1964).
[3] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Vol. II, Oxford Univ. Press, London (1946). · Zbl 0061.13505
[4] N. Rosenfeld, ?The eigenvalues of a class of singular differential operators,? Comm. Pure and Appl. Math.,13, No. 3, 395?405 (1960). · Zbl 0166.40801 · doi:10.1002/cpa.3160130305
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