Can one hear the shape of a drum? revisited
Can one hear the shape of a drum? revisited
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DOI：
10.1137/1029041
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发表时间：
1987-06
期刊：
影响因子：
10.2
通讯作者：
M. Protter
中科院分区：
文献类型：
--
作者：
M. Protter
1966年，马克·卡茨（Mark Kac）发表了一篇具有里程碑意义的论文。数学。Monthly, 73, pp. 1-23]表明通过研究拉普拉斯谱的渐近性质可以得到R^2 $中区域的几何性质。他还推测，一个区域的形状可能完全由光谱决定。我们描述了这一领域的最新发展，并讨论了Kac猜想以及除拉普拉斯算子以外的算子的类似猜想的地位。
In a landmark paper, Mark Kac in 1966 [Amer. Math. Monthly, 73, pp. 1–23] showed that geometric properties of regions in $R^2 $ can be obtained by studying the asymptotic properties of the spectrum of the Laplacian. He also conjectured that the shape of a region might be completely determined by the spectrum. We describe recent developments in this field and discuss the status of the Kac conjecture as well as similar conjectures for operators other than the Laplacian.