本文考虑由三组谱确定势函数和边值条件的问题, 即证明Sturm-Liouville问题的势函数可以由[0,1]区间上的一组整谱和[0,a], [a,1] (0 < a < 1)区间上的两组部分谱唯一确定. 特别地, 在这两个区间内, 分别可以缺失任意一个特征值, 势函数仍可以被唯一确定.

In this paper, we consider the problem of determining the potential and the boundary conditions by three spectra. That is to prove that the potential on [0,1] can be uniquely determined by a full spectrum on [0,1] and two partial spectra on [0,a] and [a,1] (0 < a < 1) respectively. On both of these two subinterval, any one of the eigenvalues can be missed in each interval respectively. After these two eigenvalues missed, the potential can also be uniquely determined.