I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1996, VOLUME 2, NUMBER 4, PAGES 1195-1204
Harmonic solution for the inverse problem of the Newtonian potential
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We study from a theoretical point of view the Backus and Gilbert
method in the case of Newtonian potential.
If a mass distribution on a open
creates a Newtonian potential , which is
known on an infinity of points out
we characterize the solution , obtained as
a generalization of the Backus and Gilbert method, as the projection
the scalar product of )
on a subspace of harmonic functions; this
subspace may be the subspace of all harmonic, square-integrable
functions (for example, if is a starlike domain).
Then we study the reproducing kernel associated to this
projection, which satisfies
for any .
Last modified: March 19, 2005