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

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.

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