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arXiv · 0906.1697

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A. D. Hemery·A. P. Veselov
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Abstract

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.

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A. D. Hemery, A. P. Veselov. 2009-07-03. Whittaker-Hill equation and semifinite-gap Schroedinger operators. https://doi.org/10.1063/1.3455367

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