{"title":"自结合无约束块雅可比矩阵的绿矩阵项的估计值","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":"{\"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}","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}
Estimates of Green matrix entries of selfadjoint unbounded block Jacobi matrices
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.