‘Can one hear the shape of a drum?’: revisited
‘Can one hear the shape of a drum?’: revisited
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DOI：
10.1088/0305-4470/38/9/l02
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发表时间：
2005-02
期刊：
影响因子：
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通讯作者：
Yuichiro Okada;A. Shudo;S. Tasaki;T. Harayama
中科院分区：
文献类型：
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作者：
Yuichiro Okada;A. Shudo;S. Tasaki;T. Harayama
M Kac 提出的一个著名的反问题“人能听到鼓的形状吗？”与鼓或平面台球的同谱性有关，第一个反例是由 Gordon、Webb 和 Wolpert 构建的（1992 Invent.Math.110 1）。在这里，我们提供了一些数字证据，表明“人们可以通过测量外部诺依曼问题的散射极来区分等谱鼓”。这是基于边界元法中出现的 Fredholm 行列式允许因式分解为内部和外部部分的观察。
A famous inverse problem posed by M Kac ‘Can one hear the shape of a drum?’ is concerned with isospectrality of drums or planer billiards, and the first counter example was constructed by Gordon, Webb and Wolpert (1992 Invent. Math. 110 1). Here we present pieces of numerical evidence showing that ‘One can distinguish isospectral drums by measuring the scattering poles of exterior Neumann problems’. This is based on the observation that the Fredholm determinant appearing in the boundary element method admits a factorization into interior and exterior parts.