|
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
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
Citation:
V. M. Gichev, “Completely reducible factors of harmonic polynomials of three variables”, Mat. Tr., 24:2 (2021), 24–36
Linking options:
https://www.mathnet.ru/eng/mt648 https://www.mathnet.ru/eng/mt/v24/i2/p24
|
Statistics & downloads: |
Abstract page: | 217 | Full-text PDF : | 66 | References: | 60 | First page: | 5 |
|