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

Abstract

The basic problem in this paper is that of detemnining the geometry of an arbitrary multiply connected bounded region in R3 together with the mixed boundary conditions, from the complete knowledge of the eigenvalues {λj}j=1∞ for the negative Laplacian, using the asymptotic expansion of the spectral function θ(t)=∑j=1∞exp(−tλj) as t→0.