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

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:

Document Type: Article
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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