Abstract
In this note we construct exampLes of a function q(x), which grows arbitrarily rapidly, and a function q(x) (c1¦x¦α ≤q (x) ≤ c2¦x¦ β, β> α >0) such that for a Sturm-Liouville operator with the constructed potential functions q (x), the classical formula for the number of eigenvalues of the operator that do not exceed λ is not true.
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M. Otelbaev, Author's Abstract of Candidate's Dissertation, Moscow State University (1972).
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Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 361–368, September, 1973.
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Otelbaev, M., Sultanaev, Y.T. On the formula for the distribution of the eigenvalues of singular differential operators. Mathematical Notes of the Academy of Sciences of the USSR 14, 768–771 (1973). https://doi.org/10.1007/BF01147452
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DOI: https://doi.org/10.1007/BF01147452