J Austral Math Soc Ser B 31 pp472--483, 1990.

On hearing the shape of an arbitrary doubly-connected region in R ²

E. M. E. Zayed

Abstract

The basic problem in this paper is that of determining the geometry of an arbitrary doubly-connected region in R ² together with an impedance condition on its inner boundary and another impedance condition on its outer boundary, from the complete knowledge of the eigenvalues {l _j}^¥_j=1 for the two-dimensional Laplacian using the asymptotic expansion of the spectral function q(t) = å^¥_j=1exp(-tl _j ) for small positive t.

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Author

E. M. E. Zayed

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