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

页码：75 / 79

页数：5

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