Geodesic
On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem
Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 708-716

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2018_104_5_a7,
     author = {M. Yu. Kokurin},
     title = {On the {Completeness} of {Products} of {Harmonic} {Functions} and the {Uniqueness} of the {Solution} of the {Inverse} {Acoustic} {Sounding} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {708--716},
     publisher = {mathdoc},
     volume = {104},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a7/}
}
TY  - JOUR
AU  - M. Yu. Kokurin
TI  - On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem
JO  - Matematičeskie zametki
PY  - 2018
SP  - 708
EP  - 716
VL  - 104
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a7/
LA  - ru
ID  - MZM_2018_104_5_a7
ER  - 
%0 Journal Article
%A M. Yu. Kokurin
%T On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem
%J Matematičeskie zametki
%D 2018
%P 708-716
%V 104
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a7/
%G ru
%F MZM_2018_104_5_a7
M. Yu. Kokurin. On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem. Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 708-716. http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a7/