arXiv subjects

S. G. Kazantsev

Publications and source records attributed to S. G. Kazantsev.

2 recordsLinked to original sources

arXiv2026

An additional possibilities of the standard method of inverting the Radon transform

The problem of inverting the Radon integral transform in finite-dimensional Euclidean space is considered. The relevance of this topic for probing issues is indicated. It is noted that for the latter direction, it is natural to consider the integrand as discontinuous function. However, the available inversion formulas are only proven for differentiable functions. Therefore, the question of obtaining formulas for discontinuous functions arises. It is set that the required results can be obtained by some modification of available proofs for smooth functions.

math-ph↗

arXiv2023

A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform

We study the problem of the integral geometry, in which the functions are integrated over hyperplanes in the $n$-dimensional Euclidean space, $n=2m+1$. The integrand is the product of a function of $n$ variables called the density and weight function depending on $2n$ 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.

math-ph↗