球谐函数与球面上的点构型
Spherical harmonics and point configurations on the sphere
AI总结：
该研究构造了极点为间距合适的点构型的二维单位球面上的球谐函数，发现当极点构型均匀分布时球谐序列呈现量子遍历性，上确界范数受极点聚类程度定量控制。
摘要：
我们构造二维单位球面上的球谐函数，方法是将高斯光束叠加，这些高斯光束的极点构成间距合适的点构型。所得球谐函数的分布性质与解析性质由这些极点的几何结构决定：当构型均匀分布时，该球谐序列呈现量子遍历性，而其上确界范数则由大圆小邻域内极点的最大聚类程度定量控制。
英文摘要：
We construct spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties of the resulting spherical harmonics are determined by the geometry of these poles: when the configuration is equidistributed, the sequence of harmonics exhibits quantum ergodicity, while their supremum norms are quantitatively controlled by the maximal clustering of poles within small neighborhoods of great circles.
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