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arXiv · 2209.03403

Spherical harmonics and point configurations on the sphere

Xiaolong Han
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Abstract

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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Xiaolong Han. 2022-09-07. Spherical harmonics and point configurations on the sphere. https://arxiv.org/abs/2209.03403

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