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The Limit Spectral Graph in the Semi-Classical Approximation for the Sturm-Liouville Problem With a Complex Polynomial Potential

The limit distribution of the discrete spectrum of the Sturm-Liouville problem with complex-valued polynomial potential 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.

preprint2016arXivOpen access
A. A. ShkalikovS. N. Tumanov
math.SP
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Open access2 authors1 topic
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A. A. ShkalikovS. N. Tumanov

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