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

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

2009-02-09

arxiv.org/abs/0902.1373v3

Geom.Funct.Anal. 20 (2010), 160-191

Mathematics

Analysis of PDEs

29 pages; some typos corrected and references added

Scientific paper

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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