Stefan Type Problem for Generalized Radon Transforms inan Even-Dimensional Space

We study a problem of integral geometry in which functions in $$2n $$ variables are integrated over hyperplanes in an $$n $$ -dimensional Euclidean space. We call such an integration the generalized Radon transform. If the integrand depends only on $$n $$ variables then this integration coincides with the classical one. In a broad sense, the problem of integral geometry is to obtain information about the integrand from the values of a family of integrals. In the present article, we consider the problem on finding the discontinuity surface of the integrand. We prove that there exists a unique solution of the problem and suggest the corresponding algorithm. It is possible to use the obtained results in the theory and practice of probing.