Three spectra inverse Sturm–Liouville problems with overlapping eigenvalues - Shouzhong Fu; Zhong Wang; Guangsheng Wei (Electronic Journal of Qualitative Theory of Differential Equations, 2017)
In the paper we show that the Dirichlet spectra of three Sturm–Liouville differential operators defined on the intervals $[0,1]$, $[0,a]$ and $[a,1]$ for some $a\in (0,1)$ fixed, together with the knowledge of the normalizing constants corresponding to the overlapped eigenvalues, uniquely determine the potential $q$ on $[0,1]$. In this situation we also provide the algorithm for recovering the potential by using the given spectral data.