, Volume 10, Issue 3, pp 628-677

Spectral determination of analytic bi-axisymmetric plane domains

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Abstract.

Let {\cal D} L denote the class of bounded, simply connected real analytic plane domains with re ection symmetries across two orthogonal axes, of which one has length L. Under generic conditions, we prove that if $ \Omega_1\Omega_2\,\in\,{\cal D}_L $ and if the Dirichlet spectra coincide, Spec $ (\Omega_1) $ = Spec $ (\Omega_2) $ , then $ \Omega_1 = \Omega_2 $ up to rigid motion.

Submitted: October 1999, Revised version: February 2000.