Hermitizable, isospectral complex second-order differential operators  

作　　者：Mu-Fa CHEN Jin-Yu LI 

机构地区：[1]Research Institute of Mathematical Science,Jiangsu Normal University,Xuzhou 221116,China [2]School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China [3]Laboratory of Mathematics and Complex Systems(Beijing Normal University),Ministry of Education,Beijing 100875,China

出　　处：《Frontiers of Mathematics in China》2020年第5期867-889,共23页中国高等学校学术文摘·数学（英文）

基　　金：supported in part by the National Natural Science Foundation of China(Grant No.11771046);the project from the Ministry of Education in China,and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

摘　　要：The first aim of the paper is to study the Hermitizability of secondorder differential operators,and then the corresponding isospectral operators.The explicit criteria for the Hermitizable or isospectral properties are presented.The second aim of the paper is to study a non-Hermitian model,which is now well known.In a regular sense,the model does not belong to the class of Hermitizable operators studied in this paper,but we will use the theory developed in the past years,to present an alternative and illustrated proof of the discreteness of its spectrum.The harmonic function plays a critical role in the study of spectrum.Two constructions of the function are presented.The required conclusion for the discrete spectrum is proved by some comparison technique.

关 键 词：Hermitizable ISOSPECTRAL differential operators non-Hermitianmodel discrete spectrum 

分 类 号：O17[理学—数学]