Asymptotics and estimates for the discrete spectrum of the Schrödinger operator on a discrete periodic graph. (English. Russian original) Zbl 1455.35161
St. Petersbg. Math. J. 32, No. 1, 9-29 (2021); translation from Algebra Anal. 32, No. 1, 12-39 (2020).
Summary: 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.
MSC:
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
| 39A12 | Discrete version of topics in analysis |
Keywords:
discrete Schrödinger operator; integral operators; estimates of singular numbers; classes of compact operatorsReferences:
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