Frontiers of Mathematics in China >
Hermitizable, isospectral complex second-order differential operators
Received date: 01 Jun 2020
Accepted date: 03 Sep 2020
Published date: 15 Oct 2020
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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.
Mu-Fa CHEN , Jin-Yu LI . Hermitizable, isospectral complex second-order differential operators[J]. Frontiers of Mathematics in China, 2020 , 15(5) : 867 -889 . DOI: 10.1007/s11464-020-0859-4
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