English

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

Analysis of PDEs 2024-04-17 v1

Abstract

In this article, we study various aspects of the mixed ray transform of (k+)(k + \ell)-tensor fields that are symmetric in its first kk 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.

Keywords

Cite

@article{arxiv.2404.10753,
  title  = {Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $\mathbb{R}^2$},
  author = {Rohit Kumar Mishra and Suman Kumar Sahoo and Chandni Thakkar},
  journal= {arXiv preprint arXiv:2404.10753},
  year   = {2024}
}