{"title":"On the Number of Components of the Essential Spectrum of One 2 × 2 Operator Matrix","authors":"M. I. Muminov, I. N. Bozorov, T. Kh. Rasulov","doi":"10.3103/s1066369x24700129","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, a <span>\\(2 \\times 2\\)</span> block operator matrix <span>\\(H\\)</span> is considered as a bounded and self-adjoint operator in a Hilbert space. The location of the essential spectrum <span>\\({{\\sigma }_{{{\\text{ess}}}}}(H)\\)</span> of operator matrix <span>\\(H\\)</span> is described via the spectrum of the generalized Friedrichs model, i.e., the two- and three-particle branches of the essential spectrum <span>\\({{\\sigma }_{{{\\text{ess}}}}}(H)\\)</span> are singled out. We prove that the essential spectrum <span>\\({{\\sigma }_{{{\\text{ess}}}}}(H)\\)</span> consists of no more than six segments (components).</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700129","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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).
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。
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
