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This article is cited in 9 scientific papers (total in 9 papers)
Research Papers
Some remarks on spherical harmonics
V. M. Gichev Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
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 $k$ nodal sets for harmonics of different degrees on $\mathbb S^m$, where $k\leq m$ (in particular, the mean number of common zeros of $m$ harmonics).
Keywords:
Nodal set, spherical harmonic, Hausdorff measure.
Received: 11.09.2007
Citation:
V. M. Gichev, “Some remarks on spherical harmonics”, Algebra i Analiz, 20:4 (2008), 64–86; St. Petersburg Math. J., 20:4 (2009), 553–567
Linking options:
https://www.mathnet.ru/eng/aa522 https://www.mathnet.ru/eng/aa/v20/i4/p64
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Abstract page: | 396 | Full-text PDF : | 135 | References: | 52 | First page: | 13 |
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