{"title":"Estimates of Green matrix entries of selfadjoint unbounded block Jacobi matrices","authors":"S. Naboko, S. Simonov","doi":"10.1090/spmj/1800","DOIUrl":null,"url":null,"abstract":"<p>In a wide class of block Jacobi matrices, the norms of Green matrix (resolvent) entries are estimated. This estimate depends on the rate of growth of the norms of the off-diagonal entries and on the distance from the spectral parameter to the essential spectrum if the latter is nonempty. The sharpness of this estimate is shown by an example.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1800","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In a wide class of block Jacobi matrices, the norms of Green matrix (resolvent) entries are estimated. This estimate depends on the rate of growth of the norms of the off-diagonal entries and on the distance from the spectral parameter to the essential spectrum if the latter is nonempty. The sharpness of this estimate is shown by an example.
期刊介绍：
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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