Geodesic
On the completeness of products of solutions to the Helmholtz equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 30-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {On the completeness of products of solutions to the {Helmholtz} equation},
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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/

[1] Calderon A.–P., “On an inverse boundary value problem”, Seminar on Numerical Anal. Appl. Continuum Phys., Sociedade Brasileira de Matem., Rio de Janeiro, 1980, 65–73 | MR

[2] Isakov V., Inverse problems for partial differential equations, Springer, N.Y., 2006 | MR | Zbl

[3] Kenig C., Salo M., “Recent progress in the Calderon problem with partial data”, Inverse probl. and appl., Contemporary math., 615, AMS, Providence, R.I., 2014, 193–222 | DOI | MR | Zbl

[4] Ditkin V. A., Prudnikov A. P., Integralnye preobrazovaniya i operatsionnoe ischislenie, GIFML, M., 1961

[5] Kipriyanov I. A., Singulyarnye ellipticheskie kraevye zadachi, Nauka, Fizmatlit, M., 1997 | MR

[6] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974

[7] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR

[8] Kokurin M. Yu., “O polnote proizvedenii garmonicheskikh funktsii i edinstvennosti resheniya obratnoi zadachi akusticheskogo zondirovaniya”, Matem. zametki, 104:5 (2018), 708–716 | MR | Zbl