Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition (Q2232087)

The paper under review deals with the half-line Neumann problem for the equation \[-y''+ x^2 y + q(x) y = \lambda y\] under some smoothness and integrability conditions on \(q\). The authors consider the inverse problem of recovering this boundary value problem by its spectrum and norming constants. They obtain a Gelfand-Levitan-Marchenko-type integral equation, prove its unique solvability, and indicate a constructive algorithm for recovering \(q\).