标题:Spectra of a class of non-symmetric operators in Hilbert spaces with applications to singular differential operators
作者:Sun H.; Xie B.
作者机构:[Sun, H] Department of Mathematics, Shandong University at Weihai Weihai, Shandong, 264209, China;[ Xie, B] Department of Mathematics, Shandong Univer 更多
通讯作者:Sun, H(sunhuaqing@email.sdu.edu.cn)
通讯作者地址:[Sun, H] Department of Mathematics, Shandong University at Weihai WeihaiChina;
来源:Proceedings of the Royal Society of Edinburgh Section A: Mathematics
出版年:2019
DOI:10.1017/prm.2018.110
关键词:defect index; eigenvalue; essential spectrum; singular Hamiltonian system; symmetric operator
摘要:This paper is concerned with a class of non-symmetric operators, that is, -symmetric operators, in Hilbert spaces. A sufficient condition for C being an element of the essential spectrum of a -symmetric operator is given in terms of the number of linearly independent solutions of a certain homogeneous equation, and a characterization for points of the essential spectrum plus the set of all eigenvalues of a -symmetric operator is obtained in terms of the numbers of linearly independent solutions of certain inhomogeneous equations. As direct applications, the corresponding results are obtained for singular -symmetric Hamiltonian systems and their special forms of singular Sturm-Liouville equations with complex-valued coefficients, which enable us to study the spectra of singular -symmetric differential expressions using numerous tools available in the fundamental theory of differential equations. Copyright © Royal Society of Edinburgh 2019.
收录类别:SCOPUS
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85061672072&doi=10.1017%2fprm.2018.110&partnerID=40&md5=2303d7defc8127d335b69c310ca1a41e
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