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On the Completeness of Products of Solutions to the Helmholtz Equation

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Abstract

We prove the completeness in L2(D) of the family of all pairwise products of solutions to the Helmholtz equation that are regular in a bounded domain D ⊂ ℝ3 and fundamental solutions to this equation with singularities at points located on the straight line \({\cal L} \subset {ℝ^3},\overline D \cap {\cal L} = \emptyset \).

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Funding

This work was performed in the framework of the state task of the Ministry of Education and Science of the Russian Federation for the Mari State University (project 1.5420.2017/8.9).

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Authors and Affiliations

  1. Mari State University, 1 Lenin sqr., Yoshkar-Ola, 424001, Russia

    M. Yu. Kokurin

Authors
  1. M. Yu. Kokurin
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Correspondence to M. Yu. Kokurin.

Additional information

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 6, pp. 30–35.

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Kokurin, M.Y. On the Completeness of Products of Solutions to the Helmholtz Equation. Russ Math. 64, 24–28 (2020). https://doi.org/10.3103/S1066369X20060055

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  • DOI: https://doi.org/10.3103/S1066369X20060055

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