On Spectral Properties of the Discrete Schrodinger Operator with Pure Imaginary Finite Potential

被引：0

作者：

Faddeev, M. M. ^{[1
]}

机构：

[1] St Petersburg State Univ, St Petersburg, Russia

来源：

MATHEMATICAL NOTES | 2009年 / 85卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

discrete Schrodinger operator; spectral problem; PJ-symmetric potential; similarity to a self-adjoint operator; HERMITICITY;

D O I：

10.1134/S0001434609030146

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the spectral properties of the discrete Schrodinger operator in the space of square integrable two-sided sequences with a pure imaginary potential of Finite rank with zero mean value. We show that if such potentials are small, then the spectrum of the operator under study coincides with the spectrum of the unperturbed operator, and the operator itself is similar to a self-adjoint operator.

引用

页码：437 / 440

页数：4

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