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arXiv · 0902.1373

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

Hamid Hezari·Steve Zelditch
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Abstract

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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Hamid Hezari, Steve Zelditch. 2009-02-09. Inverse spectral problem for analytic $(Z/2Z)^n$-symmetric domains in $R^n$. https://arxiv.org/abs/0902.1373

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