St. Petersburg Mathematical Journal

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ISSN 1547-7371(e) ISSN 1061-0022(p)

Some remarks on spherical harmonics

Author(s): V. M. Gichev
Translated by: the author
Original publication: Algebra i Analiz, tom 20 (2008), nomer 4.
Journal: St. Petersburg Math. J. 20 (2009), 553-567.
MSC (2000): Primary 33E30
Posted: June 1, 2009
MathSciNet review: 2473744
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Several observations on spherical harmonics and their nodal sets are presented: a construction for harmonics with prescribed zeros; a natural representation for harmonics on $\mathbb{S}^2$ ; upper and lower bounds for the nodal length and the inner radius (the upper bounds are sharp); the sharp upper bound for the number of common zeros of two spherical harmonics on $\mathbb{S}^2$ ; the mean Hausdorff measure of the intersection of nodal sets for harmonics of different degrees on $\mathbb{S}^m$ , where $k\leq m$ (in particular, the mean number of common zeros of harmonics).

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