On the Spectrum of a Non-Self-Adjoint Quasiperiodic Operator

被引:0
作者
Borisov, D., I [1 ,2 ,3 ]
Fedotov, A. A. [4 ]
机构
[1] Russian Acad Sci, Ufa Fed Res Ctr, Inst Math, Ufa, Russia
[2] Bashkir State Univ, Ufa, Russia
[3] Univ Hradec Kralove, Hradec Kralove, Czech Republic
[4] St Petersburg State Univ, St Petersburg, Russia
基金
俄罗斯科学基金会;
关键词
quasiperiodic operator; non-self-adjoint operator; Lyapunov exponent; spectrum; SCHRODINGER-OPERATORS;
D O I
10.1134/S1064562421060053
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the operator A, acting in l(2) (Z) by the formula (A,u)(l) = u(l+1) + u(l-1) + lambda e(-2 pi i(theta+omega l))ul. Here, / is an integer variable, while lambda > 0, theta is an element of [0,1), and omega is an element of (0,1) are parameters. For omega is not an element of Q this is the simplest non-self-adjoint quasiperiodic operator. By means of a renormalization technique, we describe the geometry of the spectrum of this operator, compute the Lyapunov exponent on the spectrum, and describe the conditions under which either the spectrum is pure continuous or a point spectrum appears additionally.
引用
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页码:326 / 331
页数:6
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