Function analysis
Daghestan Electronic Mathematical Reports: Issue 1 (2014)
Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data
UDK: 517.4
Pages: 56 - 70
DOI: 10.31029/demr.1.2
A symmetric tensor field in Euclidian space of any dimension ${{\mathbb R}}^n$ can be reconstructed from its integrals along straight lines which form n-manifold. We obtained the new formulas reconstructing solenoidal part of the fields when a ray transform is known only on complex lines, intersecting a given curve, as well as a curve belonging to infinity. The new family of two-dimensional
planes in ${{\mathbb R}}^n$ is introduced and the inversion formula is obtained for the case of differential forms of degree 2 on the given integrals along the planes of this family.
Keywords: symmetric tensor field, ray transform, reconstruction, complex of lines, solenoidal part, Radon transform of differential forms.