一类半直线上Schrödinger算子逆传输特征值问题的稳定性

Stability of the Inverse Transmission Eigenvalue Problem for the Schrodinger Operator on the Half Line

本文研究具有Neumann边界条件的Schrödinger算子逆传输特征值问题的稳定性.当∫_(0)^(1)q(t)dt=0且q(1)≠0时,存在无穷多个实传输特征值.本文在此条件下,运用变换算子理论和Riesz基相关性质,根据谱数据之差给出弱意义和W21范数意义下两势函数差的估计,这些估计蕴含了逆谱稳定性.

We study the stability of the inverse transmission eigenvalue problem for the Schr?dinger operator with the Neumann boundary condition.When∫_(0)^(1) q(t)dt=0and q(1)≠0,there are infinitely many real eigenvalues.In case,by using the theory of transformation operators and the properties of Riesz basis,we give the estimates for the difference of two potentials in the sense of the weak form and W_2~1-norm,according to the difference of two corresponding spectral data,which imply the stability of the inverse spectral problem.