Inverse Sturm–Liouville problems with the potential known on an interior subinterval
Inverse Sturm–Liouville problems with the potential known on an interior subinterval
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DOI：
10.1080/00036811.2014.915521
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发表时间：
2015-05
影响因子：
1.1
通讯作者：
Yongxia Guo;Guangsheng Wei
中科院分区：
文献类型：
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作者：
Yongxia Guo;Guangsheng Wei
研究了内部子区间上位势已知的Sturm-Liouville逆问题的唯一性问题。我们证明了整个区间和边界条件上的势是根据已知的特征值和关于内点(内谱数据)特征函数的一些信息唯一确定的。此外，我们还讨论了位势Q在某些给定点是C2k-光滑性的情形。
The uniqueness problem of inverse Sturm–Liouville problems with the potential known on an interior subinterval is considered. We prove that the potential on the entire interval and boundary conditions are uniquely determined in terms of the known eigenvalues and some information on the eigenfunctions at some interior point (interior spectral data). Moreover, we also concern with the situation where the potential q is C2k-smoothness at some given points.