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On range condition of the tensor x-ray transform in $ \mathbb R^n $

  • * Corresponding author: Aleksander Denisiuk

    * Corresponding author: Aleksander Denisiuk
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  • Consider the problem of the range description of the tensor x-ray transform in $ \mathbb R^n $, $ n\ge3 $. In this paper we use the relation between the x-ray transform and the Radon transform to obtain a geometrical interpretation of the range condition and related John differential operator. As a corollary, it is proved that the range of the $ m $-tensor x-ray transform in $ \mathbb R^n $ can be described by $ \binom{n+m-2}{m+1} $ linear differential equations of order $ 2(m+1) $.

    Mathematics Subject Classification: Primary: 44A12; Secondary: 53A45.


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