Some remarks on spherical harmonics
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V. M. Gichev
Translated by: the author - St. Petersburg Math. J. 20 (2009), 553-567
- DOI: https://doi.org/10.1090/S1061-0022-09-01061-9
- Published electronically: June 1, 2009
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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).References
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Bibliographic Information
- V. M. Gichev
- Affiliation: Omsk Division, Sobolev Mathematical Institute, Siberian Branch, Russian Academy of Sciences, Ul. Pevtsova 13, 644099 Omsk, Russia
- Email: gichev@ofim.oscsbras.ru
- Received by editor(s): September 11, 2007
- Published electronically: June 1, 2009
- Additional Notes: Supported in part by RFBR (grant nos. 06008-01403 and 06007-8951), and also by Sibirean Department of RAS (project no. 117)
- © Copyright 2009 American Mathematical Society
- Journal: St. Petersburg Math. J. 20 (2009), 553-567
- MSC (2000): Primary 33E30
- DOI: https://doi.org/10.1090/S1061-0022-09-01061-9
- MathSciNet review: 2473744