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

A. A. Shkalikov; S. N. Tumanov

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arXiv · 1603.08905

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

A. A. Shkalikov·S. N. Tumanov

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Abstract

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.

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A. A. Shkalikov, S. N. Tumanov. 2016-03-29. The Limit Spectral Graph in the Semi-Classical Approximation for the Sturm-Liouville Problem With a Complex Polynomial Potential. https://arxiv.org/abs/1603.08905

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