International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 485-492
doi:10.1155/S0161171293000596
An inverse eigenvalue problem for an arbitrary multiply connected bounded region: An extension to higher dimensions
E.M.E. Zayed
Mathematics Department, Faculty of Science, Zagazig University, Zagasig, Egypt
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.