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

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

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 25, 1-10

Abstract:

The spectral function μ ˆ ( t ) = ∑ j = 1 ∞ exp ( − i t μ j 1 / 2 ) , where { μ j } 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 μ ˆ ( 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 ℝ 2 together with Robin boundary conditions on its boundaries.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:861895

DOI: 10.1155/S0161171201005300

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