Theorem on the uniqueness of a solution of inverse problems of spectral analysis (Q1589188)

The authors are concerned with the eigenvalue problem \[ \begin{alignedat}{2} -\Delta u(x) &+q(x)u(x)=\lambda u(x),\quad &&x\in\Omega,\\ u(x) &=0,\quad &&x\in\partial\Omega,\end{alignedat} \] \(\Omega\subset \mathbb{R}^3\) is a bounded domain with piecewise \(C^2\)-boundary, \(q(x)\) is real continuous, \(\lambda\) is complex. Under some conditions involving the normal derivatives of eigenfunctions the authors prove that \(q\) is uniquely determined from eigenvalues.