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arXiv · 0705.2547

Some remarks on spherical harmonics

V. M. Gichev
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Abstract

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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V. M. Gichev. 2008-08-06. Some remarks on spherical harmonics. https://arxiv.org/abs/0705.2547

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