对称型势函数的逆谱问题  

Inverse Spectral Problems of Symmetric Potential Functions

作　　者：王文静 WANG Wenjing(College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《河南大学学报（自然科学版）》2019年第6期751-756,共6页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(11171198)

摘　　要：考虑定义在[0,1]区间上的Sturm-Liouville(S-L)微分算子的逆特征值问题.应用Weyl函数性质及Marchenko唯一性定理证明:若势函数是多重对称且在部分区间上已知,则可选取一组适当的特征值唯一确定[0,1]上的势函数.In this paper, we consider the uniqueness problem of inverse Sturm-Liouville(S-L) differential operators defined on the interval [0,1]. Making use of Weyl function and Marchenko’s uniqueness theorem, it is shown that if the potential function q(x) is multiple, symmetric and is known on some intervals, then the potential function q(x) on the interval [0,1] can be uniquely determined in terms of choosing a set of appropriate common eigenvalues.

关 键 词：Sturm-Liouville微分算子 WEYL函数 势函数 对称 特征值 

分 类 号：O175.1[理学—数学]