Inverse Sturm-Liouville problem with spectral polynomials in nonsplitting boundary conditions (Q2358640)

The boundary value problem \(L\) of the form \[ -y''+q(x)y=\lambda y,\; q\in L(0,\pi), \] \[ y'(0)-h y(0)+a(\lambda)y(\pi)=0,\; y'(\pi)+H(\lambda)y(\pi)+b(\lambda)y(0)=0 \] is considered, where \(H, a\) and \(b\) are polynomials in \(\lambda\). The authors study the inverse problem of recovering \(a(\lambda)\) and \(b(\lambda)\) from the given eigenvalues of \(L\), provided that \(q(x)\), \(H(\lambda)\) and \(h\) are known a priori. Uniqueness results are obtained for this class of inverse problems.