Abstract:
We consider the ray transform $I_\Gamma$ that integrates symmetric rank $m$ tensor fields on $\mathbb{R}^n$ supported in a bounded convex domain $D \subset \mathbb{R}^n$ over lines. The integrals are known for the family $\Gamma$ of lines $l$ such that endpoints of the segment $l \cap D$ belong to a given part $\gamma = \partial D \cap \mathbb{R}^n_{+}$ of the boundary, for some half-space $R^n_{+}\subset \mathbb{R}^n$. In this work, we assume that the domain $D$ is convex with a non-smooth boundary. In this case, we prove that the kernel of the operator $I_\Gamma$ coincides with the space of $\gamma$-potential tensor fields, which is a generalization of the results obtained in [2].
Keywords:tomography with incomplete data, ray transform, tensor analysis.
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