On a generalization of the three spectral inverse problem (Q2822226)

In the inverse problem with three given spectra, a Sturm-Liouville potential on \((0,a)\) is restored, given the spectra of the Dirichlet problem on \((0,a), (0,a/2)\), and \((a/2,a)\); see [\textit{V. N. Pivovarchik}, Integral Equations Oper. Theory 34, No. 2, 234--243 (1999; Zbl 0948.34014)]. The authors consider the case with the given spectrum of the ``Dirichlet-Dirichlet'' problem (that is the problem with Dirichlet conditions at both ends) and parts of spectra of the Dirichlet-Dirichlet and Dirichlet-Neumann problems on \((0,a/2)\) and \((a/2,a)\). This setting resembles the inverse problem by \textit{H. Hochstadt} and \textit{B. Lieberman} [SIAM J. Appl. Math. 34, 676--680 (1978; Zbl 0418.34032)].