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

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-06-04 DOI:10.3103/s1066369x24700129

M. I. Muminov, I. N. Bozorov, T. Kh. Rasulov

引用次数: 0

Abstract

In this paper, a \(2 \times 2\) block operator matrix \(H\) is considered as a bounded and self-adjoint operator in a Hilbert space. The location of the essential spectrum \({{\sigma }_{{{\text{ess}}}}}(H)\) 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 \({{\sigma }_{{{\text{ess}}}}}(H)\) are singled out. We prove that the essential spectrum \({{\sigma }_{{{\text{ess}}}}}(H)\) consists of no more than six segments (components).

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论一个 2 × 2 算子矩阵的基本频谱成分数

Abstract In this paper, a \(2 \times 2\) block operator matrix \(H\) is considered as a bounded and self-adjoint operator in a Hilbert space.通过广义弗里德里希模型的谱来描述算子矩阵 \({{\sigma }_{{{text{ess}}}}}(H)\) 的本质谱位置，即挑出本质谱 \({{\sigma }_{{{text{ess}}}}}(H)\) 的两粒子和三粒子分支。我们证明本质谱（{{\sigma }_{{text{ess}}}}}(H)\）由不超过六个段（成分）组成。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.