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
通讯作者地址：[Sun, H] Department of Mathematics, Shandong University at Weihai WeihaiChina;
来源：Proceedings of the Royal Society of Edinburgh Section A: Mathematics
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.