On the Number of Components of the Essential Spectrum of One 2 x 2 Operator Matrix

被引：0
|
作者：
Muminov, M. I. [1 ]
Bozorov, I. N. [2 ]
Rasulov, T. Kh. [3 ]
机构：
[1] Samarkand State Univ, Samarkand 140104, Uzbekistan
[2] Acad Sci Uzbek, Romanovsky Inst Math, Tashkent 100174, Uzbekistan
[3] Bukhara State Univ, Bukhara 200118, Uzbekistan
来源：
RUSSIAN MATHEMATICS | 2024年 / 68卷 / 02期
关键词：
block operator matrix; eigenvalue; discrete spectrum; essential spectrum; component; SPIN-BOSON MODEL; EIGENVALUES; LOCATION;
D O I：
10.3103/S1066369X24700129
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, a 2 x 2 block operator matrix H is considered as a bounded and self-adjoint operator in a Hilbert space. The location of the essential spectrum sigma(ess)(H) of operator matrix H is described via the spectrum of the generalized Friedrichs model, i.e., the two- and three-particle branches of the essential spectrum sigma(ess)(H) are singled out. We prove that the essential spectrum sigma(ess)(H) consists of no more than six segments (components).
引用
收藏
页码：75 / 79
页数：5
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