International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 571-580
doi:10.1155/S0161171291000777
An inverse eigenvalue problem for an arbitrary multiply connected bounded region in R2
E.M.E. Zayed
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
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.