An inverse eigenvalue problem for an arbitrary multiply connected bounded region: An extension to higher dimensions (Q687853)

Summary: The basic problem is that of determining the geometry of an arbitrary multiply connected bounded region in \(\mathbb{R}^ 3\) together with the mixed boundary conditions, from the complete knowledge of the eigenvalues \(\{\lambda_ j\}^ \infty_{j=1}\) for the negative Laplacian, using the asymptotic expansion of the spectral function \(\Theta(t)= \sum^ \infty_{j=1} \exp(-t\lambda_ j)\) as \(t\to 0\).