THE INTERLACING OF SPECTRA BETWEEN CONTINUOUS AND DISCONTINUOUS STURM-LIOUVILLE PROBLEMS AND ITS APPLICATION TO INVERSE PROBLEMS
THE INTERLACING OF SPECTRA BETWEEN CONTINUOUS AND DISCONTINUOUS STURM-LIOUVILLE PROBLEMS AND ITS APPLICATION TO INVERSE PROBLEMS
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DOI：
10.11650/tjm.1792
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发表时间：
2012-01
影响因子：
0.4
通讯作者：
Shouzhong Fu;Zongben Xu;Guangsheng Wei
中科院分区：
文献类型：
--
作者：
Shouzhong Fu;Zongben Xu;Guangsheng Wei
考虑在$[0,1]$上定义的不连续Sturm-Liouville问题，该问题在点$d\in(0,1)$处具有跳跃条件。给出了不连续Sturm-Liouville问题与$[0,d]$和$[d,1]$上定义的两个Sturm-Liouville问题之间谱的交错。作为对逆问题的应用，我们证明了势是由不连续Sturm-Liouville问题和定义在$[0,d]$和$[d,1]$上的两个Sturm-Liouville问题所产生的三个谱唯一确定的。
The discontinuous Sturm-Liouville problem defined on $[0,1]$ with jump conditions at point $d\in (0,1)$ is considered. The interlacing of the spectra between the discontinuous Sturm-Liouville problem and two Sturm-Liouville problems defined on $[0,d]$ and $[d,1]$ is provided. As the application of this interlacing to inverse problems, we prove that the potential is determined uniquely by the three spectra generated by the discontinuous Sturm-Liouville problem and two Sturm-Liouville problems defined on $[0,d]$ and $[d,1]$.