International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 571-579
doi:10.1155/S0161171291000777

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

E. M. E. Zayed1,2

1Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
2Mathematics Department, Faculty of Science, University of Emirates, P.O. Box 15551, Al-Ain, United Arab Emirates

Received 26 June 1990; Revised 26 July 1990

Copyright © 1991 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.

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.