Equivalence of inverse Sturm--Liouville problems with boundary conditions rationally dependent on the eigenparameter. (Q1426079)

Inverse spectral problems are considered for the boundary value problem \[ -y''+q(x)y=\lambda y,\quad 0<x<1, \] \[ y(0)\cos\alpha=y'(0)\sin\alpha,\quad y'(1)=f(\lambda)y(1). \] Here, \(q\in AC[0,1]\), \(\alpha\in[0,\pi)\), \(f(\lambda)=h(\lambda)/g(\lambda)\), where \(g\) and \(h\) are polynomials with real coefficients and no common zeros. Uniqueness theorems are proved for two inverse problems of recovering the potential \(q\) and the coefficients of the boundary conditions from the Weyl function and from two spectra.