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Matematicheskie Trudy, 2021, Volume 24, Number 2, Pages 24–36
DOI: https://doi.org/10.33048/mattrudy.2021.24.202
(Mi mt648)
 

Completely reducible factors of harmonic polynomials of three variables

V. M. Gichev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
References:
Abstract: We describe the divisors of complex valued homogeneous harmonic polynomials on $\mathbb R^{3}$ which are products of linear forms and characterize the homogeneous polynomials $p$ that admit a couple of linear forms $\ell_{1}$ and $\ell_{2}$ such that $\ell_{1}^{m}p$ and $\ell_{2}^{m}p$ are harmonic for some $m\in\mathbb N$. The latter gives an example of a pair of spherical harmonics whose set of common zeros has length that is compatible with the upper bound of this quantity for a single harmonic.
Key words: spherical harmonics, divisibility of harmonic polynomials.
Received: 04.04.2020
Revised: 29.06.2020
Accepted: 07.07.2020
Document Type: Article
UDC: 517.57
Language: Russian
Citation: V. M. Gichev, “Completely reducible factors of harmonic polynomials of three variables”, Mat. Tr., 24:2 (2021), 24–36
Citation in format AMSBIB
\Bibitem{Gic21}
\by V.~M.~Gichev
\paper Completely reducible factors of harmonic polynomials of three variables
\jour Mat. Tr.
\yr 2021
\vol 24
\issue 2
\pages 24--36
\mathnet{http://mi.mathnet.ru/mt648}
\crossref{https://doi.org/10.33048/mattrudy.2021.24.202}
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    Математические труды Siberian Advances in Mathematics
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