J-selfadjointness of a class of high-order differential operators with transmission conditions

Abstract

This paper is to investigate the J-selfadjointness of a class of high-order complex coefficients differential operators with transmission conditions. Using the Lagrange bilinear form of J-symmetric differential equations, the definition of J-selfadjoint differential operators and the method of matrix representation, we prove that the operator is J-selfadjoint operator, and the eigenvectors and eigen-subspaces corresponding to different eigenvalues are C-orthogonal.

Keywords

High-order differential operator / transmission conditions / J-selfadjoint / C-orthogonal

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Higher Education Press 2022