English

On the Range Characterization of the two dimensional attenuated Doppler Transform

Analysis of PDEs 2014-11-19 v1

Abstract

We characterize the range of the attenuated and non-attenuated XX-ray transform of compactly supported vector fields in the plane. The characterization is in terms of a Hilbert transform associated with the AA-analytic functions \`{a} la Bukhgeim. As an application we determine necessary and sufficient conditions for the attenuated Doppler and XX-ray data to be mistaken for each other.

Cite

@article{arxiv.1411.4923,
  title  = {On the Range Characterization of the two dimensional attenuated Doppler Transform},
  author = {Kamran Sadiq and Alexandru Tamasan},
  journal= {arXiv preprint arXiv:1411.4923},
  year   = {2014}
}
R2 v1 2026-06-22T07:03:17.145Z