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

E. L. Korotyaev ; V. A. Sloushch

Algebra i analiz, Tome 32 (2020) no. 1, pp. 12-39.

Résumé

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.

Détail

Keywords: discrete Schrödinger operator, integral operators, estimates of singular numbers, classes of compact operators.

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