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Mat. Zametki, 2018, Volume 104, Issue 5, Pages 708–716 (Mi mz11840)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem

M. Yu. Kokurin

Mari State University, Ioshkar-Ola

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00039a
Ministry of Education and Science of the Russian Federation 1.5420.2017/8.9
This work was carried out under State Contract no. 1.5420.2017/8.9 for Mari State University and supported by the Russian Foundation for Basic Research under grant 16-01-00039a.


DOI: https://doi.org/10.4213/mzm11840

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English version:
Mathematical Notes, 2018, 104:5, 689–695

Bibliographic databases:

UDC: 517.57+517.518.32+519.968.21
Received: 28.10.2017
Revised: 23.11.2017

Citation: M. Yu. Kokurin, “On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem”, Mat. Zametki, 104:5 (2018), 708–716; Math. Notes, 104:5 (2018), 689–695

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Yu. Kokurin, “O polnote proizvedenii reshenii uravneniya Gelmgoltsa”, Izv. vuzov. Matem., 2020, no. 6, 30–35  mathnet  crossref
  • Математические заметки Mathematical Notes
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