Inverse spectral problem for analytic $(Z/2Z)^n$ -symmetric domains in $R^n$

preprint2010arXivOpen access

In this paper we show that bounded analytic domains in $\R^n$ with mirror symmetries across all coordinate axes are spectrally determined among other such domains. Our approach builds on finding concrete formulas for the wave invariants at a bouncing ball orbit. The wave invariants are calculated from a stationary phase expansion applied to a well-constructed microlocal parametrix for the trace of the resolvent.

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Inverse spectral problem for analytic $(Z/2Z)^n$ -symmetric domains in $R^n$

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Inverse spectral problem for analytic (Z/2Z)n(Z/2Z)^n(Z/2Z)n-symmetric domains in RnR^nRn

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Inverse spectral problem for analytic $(Z/2Z)^n$ -symmetric domains in $R^n$