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This article is cited in 15 scientific papers (total in 15 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/mzm11840https://doi.org/10.4213/mzm11840 https://www.mathnet.ru/eng/mzm/v104/i5/p708
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Abstract page: | 319 | Full-text PDF : | 56 | References: | 33 | First page: | 11 |
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