Geometric & Functional Analysis GAFA

, Volume 10, Issue 3, pp 628–677 | Cite as

Spectral determination of analytic bi-axisymmetric plane domains

  • S. Zelditch

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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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • S. Zelditch
    • 1
  1. 1.Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA, e-mail: zel@math.jhu.edu<\EAD>US

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