Geodesic
On the completeness of products of solutions to the Helmholtz equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 30-35.

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It is established that the family of pairwise products of solutions to the Helmholtz equation regular in a bounded domain $D \subset \mathbb{R}^3$, and fundamental solutions to this equation with singularities at points from a straight line ${\mathcal{L}} \subset \mathbb{R}^3$, ${\overline{D}} \cap {\mathcal{L}}=\emptyset$, is complete in $L_2(D)$.
Keywords: Helmholtz equation, fundamental solution, harmonic function, completeness. 
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M. Yu. Kokurin. On the completeness of products of solutions to the Helmholtz equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 30-35. http://geodesic.mathdoc.fr/item/IVM_2020_6_a4/

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