关于球谐函数的几点注记
Some remarks on spherical harmonics
摘要：
本文包含了对球谐函数及其节点集的几点观察：具有指定零点的调和函数的构造;这种调和函数在$\bbS^2$上的正则表示;节点长度和内径的上界和下界（上界是尖锐的）; $\bbS^2$上两个球谐函数公共零点个数的精确上界; $\bbS^m$上不同阶谐波的$k$节点集的交点上的平均Hausdorff测度，其中$k\leq m$（特别是$m$谐波的公共零点的平均数）。
英文摘要：
The article contains several observations on spherical harmonics and their nodal sets: a construction for harmonics with prescribed zeroes; a kind of canonical representation of this type for harmonics on $\bbS^2$; upper and lower bounds for nodal length and inner radius (the upper bounds are sharp); precise upper bound for the number of common zeroes of two spherical harmonics on $\bbS^2$; the mean Hausdorff measure on the intersection of $k$ nodal sets for harmonics of different degrees on $\bbS^m$, where $k\leq m$ (in particular, the mean number of common zeroes of $m$ harmonics).
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