We study a concentration problem on the unit sphere \(\mathbb {S}^2\) for band-limited spherical harmonics expansions using large sieve methods. We derive upper bounds for concentration in terms of the maximum Nyquist density. Our proof uses estimates of the spherical harmonics coefficients of certain zonal filters. We also demonstrate an analogue of the classical large sieve inequality for spherical harmonics expansions.

中文翻译：

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通过大筛原理对带限球形调和波展开的浓度估计

我们使用大筛方法研究了带限球面谐波展开的单位球面\（\ mathbb {S} ^ 2 \）上的集中问题。我们根据最大奈奎斯特密度得出浓度的上限。我们的证明使用某些区域滤波器的球谐系数估计值。我们还证明了球谐函数展开的经典大筛不等式的类似物。