R³中等谱非等距同构分形鼓的构造及谱渐近

R 3 中等谱非等距同构分形鼓的构造及谱渐近 On the Construction of Non-Isometric Isospectral Fractal Drums in R 3 and Spectral Asymptotics 陈化 CHEN Hua 1 first-author 柯良军 KE Liang jun 1 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 School of Mathematics and Statistics,Wuhan University School of Mathematics and Statistics,Wuhan University 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 . 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. 等谱非等距同构 分形鼓 狄雷克利波数目函数 non isometric isospectral fractal drums Dirichlet counting function O175.9;O175.25 国家自然科学基金 （ 195 3 10 80 ）;华诚基金资助项目 2001-03-01 2021-04-01 3