边界条件含谱参数的S-L算子反问题

Inverse Problems for Sturm-Liouville Operators with One Boundary Condition Having the Spectral Parameter

本文用混合谱数据研究边界条件含谱参数的Sturm-Liouville算子反问题.已知[a0,1]上的势函数q(x),我们证明一组谱的部分特征值唯一确定[0,1]上的势函数q(x).此外,还证明了缺少两个特征值的一组谱也能唯一确定[0,1]上的势函数q(x).

The inverse spectral problems for Sturm-Liouville operators with one boundary condition having the spectral parameter are studied from mixed spectral data in this paper.The authors show that if the potential q(α)on[ao,1]is given a priori,then the potential q(a)on[0,1]can be uniquely determined by parts of one spectrum.In addition,we prove that the potential q(a)on[0,1]can be uniquely determined by one spectrum with two eigenvalues missing.