The Wave Equation Approach to Robbin Inverse Problems for a Doubly-Connected Region: An Extension to Higher Dimensions (Journal of Computational Mathematics, 1989)
The spectral function $\hatμ(t)=\sum\limits_{j=1}^∞ e^{-itλ^{\frac{1}{2}}_j}$ where $\{λ_j\}^∞_{j=1}$ are the eigenvalues of the three-dimensional Laplacian is studied for a variety of domains, where $- ∞＜t＜∞$ and $i=\sqrt{-1}$. The dependence of $\hat{μ}(t)$ on the connectivity of a domain and the impedance boundary condition (Robbin conditions) are analyzed. Particular attention is given to the spherical shell together with Robbin boundary conditions on its surface.