Weighted Radon transforms of three-dimensional symmetric tensor fields
0000-0001-8113-5502 The paper investigates the properties of weighted Radon transforms of symmetric 2-tensor fields in $\mathbb{R}^3$. The relationships between the weighted Radon transforms of tensor fields of rank 2 and the Radon transform of their potentials are established. These connections provide a description of kernels and images of tomographic integral operators acting on tensor fields. Variants of problem statements for the reconstruction of symmetric 2-tensor fields from the values of jointly defined normal, longitudinal and weighted Radon transforms are considered, inversion formulas are obtained.
УДК 517.44+514.8
${file_?????}Keywords: Tensor tomography, decomposition of tensor field, generalized Ra\-don transform, weighted Radon transform, inversion formula.