The reconstruction of the differential operator by its spectrum (Q1905295)

Let us consider the Sturm-Liouville equation \(ly = - y''(x) + q(x)y(x) = \lambda^2 y(x)\) with a real-valued (potential) function \(q(x)\) that belongs to the subset \(L_2' [0, \pi]\) of the space \(L_2 [0, \pi]\) such that \(q(\pi - x) = q(x)\). In this paper we investigate the inverse spectral problem for operators generated in the segment \([0, \pi]\) by the operator \(l\) and by boundary conditions of the form \(y'(0) + h[y(\pi) - y(0)] = 0\), \(y'(0) - y'(\pi) = 0\), where \(h\) is an arbitrary real number.