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Algebra i Analiz, 2008, Volume 20, Issue 4, Pages 64–86 (Mi aa522)  

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
Full-text PDF (360 kB) Citations (9)
References:
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
English version:
St. Petersburg Mathematical Journal, 2009, Volume 20, Issue 4, Pages 553–567
DOI: https://doi.org/10.1090/S1061-0022-09-01061-9
Bibliographic databases:
Document Type: Article
MSC: 33E30
Language: Russian
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
Citation in format AMSBIB
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\by V.~M.~Gichev
\paper Some remarks on spherical harmonics
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\issue 4
\pages 64--86
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\zmath{https://zbmath.org/?q=an:1206.33023}
\elib{https://elibrary.ru/item.asp?id=11568877}
\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 4
\pages 553--567
\crossref{https://doi.org/10.1090/S1061-0022-09-01061-9}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267802600003}
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  • https://www.mathnet.ru/eng/aa522
  • https://www.mathnet.ru/eng/aa/v20/i4/p64
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:396
    Full-text PDF :135
    References:52
    First page:13
     
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