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arXiv · 2211.03326

Perturbation of discriminant for one-dimensional discrete Schr\"odinger operator with sparse periodic potential

Masahiro Kaminaga
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Abstract

We consider the one-dimensional discrete Schr\"odinger operator with complex-valued sparse periodic potential. The spectrum for a complex-valued periodic potential is a complicated compact set in the complex plane represented by real intersections of algebraic curves determined by a discriminant. We represent the discriminant by Chebyshev polynomials and use perturbations of the discriminant to study the spectrum.

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Masahiro Kaminaga. 2022-11-07. Perturbation of discriminant for one-dimensional discrete Schr\"odinger operator with sparse periodic potential. https://arxiv.org/abs/2211.03326

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