标题:Approximation of eigenvalues below the essential spectra of singular second-order symmetric linear difference equations
作者:Liu Yan;Shi Yuming
作者机构:[Liu Yan] Department of Mathematics, Shandong University, Jinan, Shandong 250100, China.;[Shi Yuming] Department of Mathematics, Shandong University, 更多
通讯作者:Shi, YM(ymshi@sdu.edu.cn)
通讯作者地址:[Shi, YM]Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China.
来源:中国科学. 数学
出版年:2017
卷:60
期:9
页码:1661-1678
DOI:10.1007/s11425-016-0223-9
关键词:difference equation; approximation; eigenvalue; limit point case;; self-adjoint subspace
摘要:This paper is concerned with approximation of eigenvalues below the essential spectra of singular second-order symmetric linear difference equations with at least one endpoint in the limit point case. A sufficient condition is firstly given for that the k-th eigenvalue of a self-adjoint subspace (relation) below its essential spectrum is exactly the limit of the k-th eigenvalues of a sequence of self-adjoint subspaces. Then, by applying it to singular second-order symmetric linear difference equations, the approximation of eigenvalues below the essential spectra is obtained, i.e., for any given self-adjoint subspace extension of the corresponding minimal subspace, its k-th eigenvalue below its essential spectrum is exactly the limit of the k-th eigenvalues of a sequence of constructed induced regular self-adjoint subspace extensions.
收录类别:CSCD;SCOPUS;SCIE
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85013671327&doi=10.1007%2fs11425-016-0223-9&partnerID=40&md5=b57027b44562b4653691c8f8152ae038
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