Ray Transforms and Vector Fields
Complex Variables
2011-02-10 v1 Functional Analysis
Abstract
We review and extend a technique for recovering a smooth function from its averages over a wide class of curves in a general region of Euclidean space. The method is based on complexification of the underlying vector fields defining the transport and recasting the problem in terms of complex-analytic function theory. Conditions on the validity of prior formulae appearing in a previous paper as well as stability estimates are then discussed first for the case of vector fields with polynomial coefficients and later for more general cases.
Keywords
Cite
@article{arxiv.1102.1736,
title = {Ray Transforms and Vector Fields},
author = {Nicholas Hoell},
journal= {arXiv preprint arXiv:1102.1736},
year = {2011}
}