English

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}
}
R2 v1 2026-06-21T17:23:35.077Z