中心对称解析平面域在这类中是谱决定的
Centrally symmetric analytic plane domains are spectrally determined in this class
摘要：
我们证明了，在一些一般的非退化假设下，实解析的，中心对称的平面域是由它们的Dirichlet（分别）决定的。Neumann）谱。证明了实解析凸区域的条件是开稠密的。证明是平行的证明，上/下对称域是谱确定的。第一步是使用马斯洛夫指数计算，以表明在弹跳球轨道的端点处的中心对称域的定义函数的二阶导数是谱不变量。对于上/下对称域也是如此，在这种情况下从证明中删除了一个假设。
英文摘要：
We prove that, under some generic non-degeneracy assumptions, real analytic, centrally symmetric plane domains are determined by their Dirichlet (resp. Neumann) spectra. We prove that the conditions are open-dense for real analytic convex domains. The proof is parallel to the proof that up/down symmetric domains are spectrally determined. One step is to use a Maslov index calculation to show that the second derivative of the defining function of a centrally symmetric domain at the endpoints of a bouncing ball orbit is a spectral invariant. This is also true for up/down symmetric domains, removing an assumption from the proof in that case.
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