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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 1299–1312
DOI: https://doi.org/10.33048/semi.2020.17.096
(Mi semr1290)
 

This article is cited in 1 scientific paper (total in 1 paper)

Real, complex and functional analysis

Factorization of special harmonic polynomials of three variables

V. M. Gichev

Sobolev Institute of Mathematics, Omsk Branch, 13, Pevtsova str., Omsk, 644099, Russia
Full-text PDF (394 kB) Citations (1)
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Abstract: We consider homogeneous harmonic polynomials of real variables $x,y,z$ that are eigenfunctions of the rotations about the axis $z$. They have the form $(x\pm yi)^{n}p(x,y,z)$, where $p$ is a rotation invariant polynomial. Let $\mathfrak{R}_{m}$ be the family of the homogeneous rotation invariant polynomials $p$ of degree $m$ such that $p$ is reducible over the rationals and $(x+yi)^{n}p$ is harmonic for some $n\in\mathbb{N}$. We describe $\mathfrak{R}_{m}$ for $m\leq5$ and prove that $\mathfrak{R}_{6}$ and $\mathfrak{R}_{7}$ are finite.
Keywords: Legendre functions, harmonic polynomials, factorization.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I. 1.1., project 0314-2019-0004
The work was supported by the program of fundamental scientific research of the SB RAS I. 1.1., project 0314-2019-0004.
Received November 2, 2019, published September 8, 2020
Bibliographic databases:
Document Type: Article
UDC: 517.586, 512.622
MSC: 33C55, 33D45, 12D05
Language: English
Citation: V. M. Gichev, “Factorization of special harmonic polynomials of three variables”, Sib. Èlektron. Mat. Izv., 17 (2020), 1299–1312
Citation in format AMSBIB
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\by V.~M.~Gichev
\paper Factorization of special harmonic polynomials of three variables
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 1299--1312
\mathnet{http://mi.mathnet.ru/semr1290}
\crossref{https://doi.org/10.33048/semi.2020.17.096}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000567363400001}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Full-text PDF :49
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