Geodesic
On expansions over harmonic polynomial products in ${\mathbb R}^3$
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 36-42 
A. F. Vakulenko. On expansions over harmonic polynomial products in ${\mathbb R}^3$. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 36-42. http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a4/
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     title = {On expansions over harmonic polynomial products in~${\mathbb R}^3$},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a4/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In inverse problems, an important role is played by the following fact: the functions of the form \begin{align*} \sum_{k=1}^{n} f_k(x,y,z) g_k(x,y,z), \end{align*} where $f_k,g_k$ are the solutions of a second order elliptic equation in a bounded domain $\Omega\subset\mathbb R^3$, constitute a dense set in $L_2(\Omega)$. This paper deals with the Laplace equation. We show that the density does hold if $f_k$ and $g_k$ are harmonic polynomials, whereas the factors $g_k$ are invariant with respect to shifts or rotations.

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