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The limit spectral graph in semiclassical approximation for the Sturm–Liouville problem with complex polynomial potential

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Abstract

The limit behavior of the discrete spectrum of the Sturm–Liouville problem whose potential is a polynomial with complex coefficients on an interval, on a half-axis, and on the entire axis is studied. It is shown that, at large parameter values, the eigenvalues are concentrated along the so-called limit spectral graph; the curves forming this graph are classified. Asymptotics of eigenvalues along curves of various types in the graph are calculated.

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Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    S. N. Tumanov & A. A. Shkalikov

Authors
  1. S. N. Tumanov
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  2. A. A. Shkalikov
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Correspondence to S. N. Tumanov.

Additional information

Original Russian Text © S.N. Tumanov, A.A. Shkalikov, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 6, pp. 660–664.

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Tumanov, S.N., Shkalikov, A.A. The limit spectral graph in semiclassical approximation for the Sturm–Liouville problem with complex polynomial potential. Dokl. Math. 92, 773–777 (2015). https://doi.org/10.1134/S106456241506037X

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  • DOI: https://doi.org/10.1134/S106456241506037X

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