BibTeX
@MISC{Gichev08someremarks,
author = {V. M. Gichev},
title = {Some remarks on spherical harmonics},
year = {2008}
}
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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 natural representation of this type for harmonics on S 2; upper and lower bounds for nodal length and inner radius (the upper bounds are sharp); the precise upper bound for the number of common zeroes of two spherical harmonics on S 2; the mean Hausdorff measure on the intersection of k nodal sets for harmonics of different degrees on S m, where k ≤ m (in particular, the mean number of common zeroes of m harmonics).
