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.

Key words： High-order differential operator; transmission conditions; J-selfadjoint; C-orthogonal

Acknowledgements

This paper was supported by the National Natural Science Foundation of China (Grant No. 12261066)

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