Spectral determination of analytic axi-symmetric plane domains

Details Spectral determination of analytic axi-symmetric plane domains Spectral determination of analytic axi-symmetric plane domains

1999-01-03

arxiv.org/abs/math/9901005v2

Mathematics

Spectral Theory

Scientific paper

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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