Whittaker-Hill equation and semifinite-gap Schroedinger operators
Spectral Theory
2015-05-13 v2
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.
Cite
@article{arxiv.0906.1697,
title = {Whittaker-Hill equation and semifinite-gap Schroedinger operators},
author = {A. D. Hemery and A. P. Veselov},
journal= {arXiv preprint arXiv:0906.1697},
year = {2015}
}
Comments
Revised version