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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
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.
Received November 2, 2019, published September 8, 2020
Citation:
V. M. Gichev, “Factorization of special harmonic polynomials of three variables”, Sib. Èlektron. Mat. Izv., 17 (2020), 1299–1312
Linking options:
https://www.mathnet.ru/eng/semr1290 https://www.mathnet.ru/eng/semr/v17/p1299
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Abstract page: | 139 | Full-text PDF : | 49 | References: | 12 |
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