### 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.