International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 485-492

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

Received 30 August 1991; Revised 3 September 1992

Copyright © 1993 E. M. E. Zayed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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=1exp(tλj) as t0.