Inversion of seismic-type Radon transforms on the plane
Classical Analysis and ODEs
2020-05-26 v3 Functional Analysis
Abstract
We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of functions with a fixed axis of the independent variable, and are imposed some symmetry with respect to the axes. These transforms contain the parabolic Radon transform and the hyperbolic Radon transform arising from seismology. We prove the inversion formulas for these transforms under some vanishing and symmetry conditions of functions.
Cite
@article{arxiv.1910.02645,
title = {Inversion of seismic-type Radon transforms on the plane},
author = {Hiroyuki Chihara},
journal= {arXiv preprint arXiv:1910.02645},
year = {2020}
}
Comments
10 pages, no figure