Spectral determination of analytic axi-symmetric plane domains

Steve Zelditch

Spectral determination of analytic axi-symmetric plane domains

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arxiv math/9901005 v2 pith:2HKLQONM submitted 1999-01-03 math.SP math.AP

Steve Zelditch This is my paper · ORCID

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keywords omegaanalyticdomainsplanespecaxi-symmetricboundedclass

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abstract

Let ${\cal D}$ denote the class of bounded real analytic plane domains with the symmetry of an ellipse. We prove that if $\Omega_1, \Omega_2 \in {\cal D}$ 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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