Abstract
We describe the limiting spectrum C(L)* of the non-self-conjugate second-order differential operator L with slowly varying coefficients, defined in L2(−∞, ∞). The limiting spectrum is constructed from the spectra of operators with constant coefficients which are obtained from L by “freezing” the argument in the variable coefficients.
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I. M. Glazman, Direct Methods for the Qualitative Spectral Analysis of Singular Differential Equations [in Russian], Moscow (1963)
F. S. Rofe-Beketov, “The spectrum of non-self-conjugate differential operators with periodic coefficients,” Dokl. Akad. Nauk SSSR,152, No. 6, 1312–1315 (1963).
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Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 135–146, January, 1973.
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Zelenko, L.B. The limiting spectrum of a non-self-conjugate second-order differential operator with slowly varying coefficients. Mathematical Notes of the Academy of Sciences of the USSR 13, 80–86 (1973). https://doi.org/10.1007/BF01093636
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DOI: https://doi.org/10.1007/BF01093636