Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Some remarks on spherical harmonics


Author: 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
DOI: https://doi.org/10.1090/S1061-0022-09-01061-9
Published electronically: June 1, 2009
MathSciNet review: 2473744
Full-text PDF Free Access

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 $ 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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 33E30

Retrieve articles in all journals with MSC (2000): 33E30


Additional 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

DOI: https://doi.org/10.1090/S1061-0022-09-01061-9
Keywords: Nodal set, spherical harmonics, Hausdorff measure
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)
Article copyright: © Copyright 2009 American Mathematical Society