Asymptotics and estimates for the discrete spectrum of the Schrödinger operator on a discrete periodic graph

Korotyaev, E.; Sloushch, V.

doi:10.1090/spmj/1635

Asymptotics and estimates for the discrete spectrum of the Schrödinger operator on a discrete periodic graph
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by E. L. Korotyaev and V. A. Sloushch
Translated by: E. Peller

St. Petersburg Math. J. 32 (2021), 9-29

DOI: https://doi.org/10.1090/spmj/1635

Published electronically: January 11, 2021

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Abstract:

The periodic Schrödinger operator $H$ on a discrete periodic graph is treated. The discrete spectrum is estimated for the perturbed operator $H_{\pm }(t)=H\pm tV$, $t>0$, where $V\ge 0$ is a decaying potential. In the case when the potential has a power asymptotics at infinity, an asymptotics is obtained for the discrete spectrum of the operator $H_{\pm }(t)$ for a large coupling constant.

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