On the $X$-ray transform of symmetric higher order tensors

David Omogbhe; Kamran Sadiq

On the $X$-ray transform of symmetric higher order tensors

Analysis of PDEs 2022-10-05 v1

Authors: David Omogbhe , Kamran Sadiq

Abstract

In this article we characterize the range of the attenuated and non-attenuated $X$ -ray transform of compactly supported symmetric tensor fields in the Euclidean plane. The characterization is in terms of a Hilbert-transform associated with $A$ -analytic maps in the sense of Bukhgeim.

Keywords

x-ray transform symmetric tensor fields hilbert transform a-analytic maps euclidean plane range characterization

Cite

@article{arxiv.2210.01473,
  title  = {On the $X$-ray transform of symmetric higher order tensors},
  author = {David Omogbhe and Kamran Sadiq},
  journal= {arXiv preprint arXiv:2210.01473},
  year   = {2022}
}

Comments

29 pages. arXiv admin note: text overlap with arXiv:1503.04322

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