Isospectral sets for transmission eigenvalue problem (Q2301653)

Isospectral sets are described for the boundary value problem \[ \begin{gathered} -y''+q(x)y=\rho^2 y,\; x\in(0,1),\\ y(0)=0,\; y(1)\cos\rho-y'(1)\sin\rho/\rho=0, \end{gathered} \] where $q(x)\in L_2(0,1)$ is a complex-valued function.