An inverse problem for Sturm-Liouville operators with non-separated boundary conditions containing the spectral parameter (Q318176)

Let \(P_k\), \(k=1,2\), be the spectra of the boundary value problems \(B_k\) of the form NEWLINE\[NEWLINE -y''+q(x)y=\lambda y,\; q(x)\in L_2(0,\pi), NEWLINE\]NEWLINE NEWLINE\[NEWLINE y'(0)+(\alpha\lambda+\beta_k)y(0)+\omega y(\pi)= y'(\pi)+\gamma y(\pi)-\omega y(0)=0, NEWLINE\]NEWLINE where \(q(x),\alpha,\beta,\gamma,\omega\) are real, and \(\alpha\omega\neq 0\). The authors study the inverse problem of recovering \(B_k\) from the given two spectra \(P_k\) and an additional sequence of signs. They formulate (without proofs) the uniqueness result and and algorithm for the solution of the inverse problem.