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Asymptotics and estimates for the discrete spectrum of the Schrödinger operator on a discrete periodic graph
St. Petersburg Mathematical Journal ( IF 0.7 ) Pub Date : 2021-01-11 , DOI: 10.1090/spmj/1635 E. L. Korotyaev , V. A. Sloushch
St. Petersburg Mathematical Journal ( IF 0.7 ) Pub Date : 2021-01-11 , DOI: 10.1090/spmj/1635 E. L. Korotyaev , V. A. Sloushch
Abstract:The periodic Schrödinger operator 
on a discrete periodic graph is treated. The discrete spectrum is estimated for the perturbed operator 
, 
, where 
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 
for a large coupling constant.
中文翻译：
离散周期图上薛定ding算子离散谱的渐近性和估计
摘要：研究了离散周期图上的周期Schrödinger算子。离散谱估计的扰动算子，其中是一个衰减电势。在电势具有无穷大的渐近性的情况下，对于较大的耦合常数，对于算子的离散频谱可获得渐近性。
更新日期：2021-01-14
on a discrete periodic graph is treated. The discrete spectrum is estimated for the perturbed operator , , where 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 for a large coupling constant. 中文翻译：
离散周期图上薛定ding算子离散谱的渐近性和估计
摘要：
研究了离散周期图上的周期Schrödinger算子。离散谱估计的扰动算子，其中是一个衰减电势。在电势具有无穷大的渐近性的情况下，对于较大的耦合常数，对于算子的离散频谱可获得渐近性。 
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