# Spectral determination of analytic bi-axisymmetric plane domains

@article{Zelditch2000SpectralDO, title={Spectral determination of analytic bi-axisymmetric plane domains }, author={Steve Zelditch}, journal={Geometric \& Functional Analysis GAFA}, year={2000}, volume={10}, pages={628-677} }

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.

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