Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $\mathbb{R}^2$

Rohit Kumar Mishra; Suman Kumar Sahoo; Chandni Thakkar

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arXiv · 2404.10753

Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $\mathbb{R}^2$

Rohit Kumar Mishra·Suman Kumar Sahoo·Chandni Thakkar

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Abstract

In this article, we study various aspects of the mixed ray transform of $(k + \ell)$-tensor fields that are symmetric in its first $k$ and last $\ell$ indices. As a first result, we derive an inversion algorithm to recover the solenoidal part of the unknown tensor field using the normal operator of the mixed ray transform. Next, we establish a set of unique continuation results. In addition to these, we discuss the range characterization of the mixed ray transform as the final result.

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Rohit Kumar Mishra, Suman Kumar Sahoo, Chandni Thakkar. 2024-04-16. Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $\mathbb{R}^2$. https://arxiv.org/abs/2404.10753

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