An inverse eigenvalue problem for an arbitrary multiply connected bounded region in R2

Abstract

The basic problem is to determine the geometry of an arbitrary multiply connected bounded region in R2 together with the mixed boundary conditions, from the complete knowledge of the eigenvalues {λi}j=1∞ for the Laplace operator, using the asymptotic expansion of the spectral function θ(t)=∑j=1∞exp(−tλi) as t→0.