Inverse Transmission Eigenvalue Problems For The Schr(?)dinger Operator

The transmission eigenvalue problems for Schrodinger operator are important subjects in the theory of the acoustic wave scattering and quantum scattering,and the relevant inverse problems have important applications in nondestructive testing,medical detection and radar.The main problems considered in thesis are as follows:1.For the case of the Dirichlet boundary condition,we study the stability of the inverse spectral problems by using the transformation operator theory and the properties of the Riesz basis,and give the estimation of the difference of two potential functions controlled by the difference of spectral data;2.For the case of the Robin boundary condition:(1)according to Paley-Winner theorem,Cartwright-Levison theorem and the relevant properties of integer functions of exponential type,we study the relationship between the density of eigenvalues and the length of the support interval of the potential,and obtain the necessary and sufficient condition for the density of eigenvalues to be a certain value,which improves the research results of Colton and Leung;(2)using Hadamard factorization theorem and two-spectrum theorem to study the inverse spectral problems when the boundary condition parameters are unknown,and prove the uniqueness theorem,which further solves the open problem proposed by Aktosun and Papanicolaou;(3)we discuss the local solvability and stability of the inverse spectral problem by using successive approximation method and the properties of the Riesz basis.