Some remarks on spherical harmonics

dc.creatorGichev, V. M.
dc.date2007-05-17
dc.date2008-08-06
dc.date.accessioned2026-07-07T09:54:37Z
dc.date.available2026-07-07T09:54:37Z
dc.descriptionThe 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).
dc.description20 pages. Translation of the version which is published in Russian. Minor modifications throughout the paper. An error in calculation is corrected (page 14)
dc.identifierhttps://arxiv.org/abs/0705.2547
dc.identifierhttp://arxiv.org/abs/0705.2547
dc.identifierAlgebra i Analiz, 2008, V. 20, No 4, 64--86 (in Russian)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166382
dc.subjectClassical Analysis and ODEs
dc.subjectMetric Geometry
dc.subject58J50; 51M16
dc.titleSome remarks on spherical harmonics
dc.typetext

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