2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166382The 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).20 pages. Translation of the version which is published in Russian. Minor modifications throughout the paper. An error in calculation is corrected (page 14)Classical Analysis and ODEsMetric Geometry58J50; 51M16text