Inverse problem for singular diffusion operator

[摘要] In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary conditions and jump conditions. Some properties of eigenvalues and eigenfunctions are investigated. Asymtotic representation of eigenvalues and eigenfunction have been obtained. Reconstruction of the singular diffusion operator have been shown by the Weyl function.

[学科分类] 数学（综合）

[关键词] inverse problem;Sturm-Liouville;diffusion operator;integral representation