International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 11, Pages 717-726

The wave equation approach to an inverse eigenvalue problem for an arbitrary multiply connected drum in 2 with Robin boundary conditions

E. M. E. Zayed and I. H. Abdel-Halim

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

Received 25 June 1999

Copyright © 2001 E. M. E. Zayed and I. H. Abdel-Halim. 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 spectral function μˆ(t)=j=1exp(itμj1/2), where {μj}j=1 are the eigenvalues of the two-dimensional negative Laplacian, is studied for small |t| for a variety of domains, where <t< and i=1. The dependencies of μˆ(t) on the connectivity of a domain and the Robin boundary conditions are analyzed. Particular attention is given to an arbitrary multiply-connected drum in 2 together with Robin boundary conditions on its boundaries.