On The X-Ray Transform Of Planar Symmetric 2-Tensors

Keywords

A-analytic maps; Attenuated X-ray transform; Boundary rigidity problem; Hilbert transform; X-ray transform of symmetric tensors

Abstract

In this paper we study the attenuated X-ray transform of 2-tensors supported in convex bounded subsets with sufficiently smooth boundary in the Euclidean plane. We characterize its range and reconstruct all possible 2-tensors yielding identical X-ray data. The characterization is in terms of a Hilbert-transform associated with A-analytic maps in the sense of Bukhgeim.

Publication Date

10-1-2016

Publication Title

Journal of Mathematical Analysis and Applications

Volume

442

Issue

1

Number of Pages

31-49

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmaa.2016.04.018

Socpus ID

84964608819 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84964608819

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