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

作　　者：马利杰 郭燕 徐小川 Li Jie MA;Yan GUO;Xiao Chuan XU(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,P.R.China;Center for Applied Mathematics of Jiangsu Province,Nanjing University of Information Science and Technology,Nanjing 210044,P.R.China;Jiangsu International Joint Laboratory on System Modeling and Data Analysis,Nanjing University of Information Science and Technology,Nanjing 210044,P.R.China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044 [2]南京信息工程大学江苏省应用数学中心,南京210044 [3]南京信息工程大学江苏省系统建模与数据分析国际合作联合实验室,南京210044

出　　处：《数学学报（中文版）》2024年第1期72-88,共17页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11901304);江苏省研究生科研与实践创新计划项目(KYCX22_1126)。

摘　　要：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.

关 键 词：逆谱问题 Schrödinger算子 传输特征值问题 稳定性 有限谱数据 

分 类 号：O175.3[理学—数学]