Affiliation:
1. Sobolev Institute of Mathematics , Novosibirsk , Russia
Abstract
Abstract
We study the problem of the integral geometry, in which
the functions are integrated over hyperplanes in the n-dimensional Euclidean
space,
n
=
2
m
+
1
{n=2m+1}
. The integrand is the product of a function of n variables called the density and
weight function depending on
2
n
{2n}
variables. Such an integration is called here the weighted Radon transform,
which coincides with the classical one if the weight function is equal to one. It is proved the uniqueness for the problem of determination of the surface on which the integrand is
discontinuous.
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