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

Aleksander Denisiuk

doi:10.3934/ipi.2020020

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2020, Volume 14, Issue 3: 423-435. Doi: 10.3934/ipi.2020020

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

Aleksander Denisiuk^,

University of Warmia and Mazury, Faculty of Mathematics and Computer Science, ul. Słoneczna 54, 10-710 Olsztyn, Poland

^* Corresponding author: Aleksander Denisiuk
^* Corresponding author: Aleksander Denisiuk

Received: March 31, 2019

Revised: October 31, 2019

Published: March 2020

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Abstract

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) $.

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

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References

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