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 -ray transform of compactly supported vector fields in the plane. The characterization is in terms of a Hilbert transform associated with the -analytic functions \`{a} la Bukhgeim. As an application we determine necessary and sufficient conditions for the attenuated Doppler and -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}
}