Geodesic
On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem
Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 708-716.

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It is proved that the family of all pairwise products of regular harmonic functions on $D$ and of the Newtonian potentials of points on the line $L\subset\mathbb R^n$ is complete in $L_2(D)$, where $D$ is a bounded domain in $\mathbb R^n$, $n\ge 3$, such that $\overline D\cap L=\varnothing$. This result is used in the proof of uniqueness theorems for the inverse acoustic sounding problem in $\mathbb R^3$.
Keywords: harmonic function, Newtonian potential, completeness, integral equation, acoustic sounding, inverse problem, unique solvability. 
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M. Yu. Kokurin. On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem. Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 708-716. http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a7/

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