| R~3中等谱非等距同构分形鼓的构造及谱渐近 |
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| 引用本文： | 陈化,柯良军.R~3中等谱非等距同构分形鼓的构造及谱渐近[J].武汉大学学报(理学版),2001(3). |
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| 作者姓名： | 陈化 柯良军 |
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| 作者单位： | 武汉大学数学与统计学院!湖北武汉430072 |
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| 基金项目： | 国家自然科学基金 ( 195 3 10 80 )，华诚基金资助项目 |
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| 摘 要： | 在 R3中构造了一对等谱非等距同构分形鼓 .在此基础上 ,研究了其对应的狄雷克利波数目函数的渐近性态 ,并且证明其波数目函数有精确的第二项估计 ,同时对其第二项渐近系数的上界和下界进行了估计 ,结果表明 Wegl- Berrg猜想是不适合此例的 .
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| 关 键 词： | 等谱非等距同构 分形鼓 狄雷克利波数目函数 |
On the Construction of Non-Isometric Isospectral Fractal Drums in R~3 and Spectral Asymptotics |
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| CHEN Hua,KE Liang jun.On the Construction of Non-Isometric Isospectral Fractal Drums in R~3 and Spectral Asymptotics[J].JOurnal of Wuhan University:Natural Science Edition,2001(3). |
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| Authors: | CHEN Hua KE Liang jun |
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| Abstract: | We construct a pair of disjoint non isometric isospectral fractal drums in R 3, in which the boundaries have the same Minkowski dimension. We also estimate the second asymptotic term for the Dirichlet counting function and obtain the exact second term and two side sharp estimates for the remainder term of the counting function.Our result shows Weyl\|Berry conjecture is not true for the case here. |
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| Keywords: | non isometric isospectral fractal drums Dirichlet counting function |
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