Spherical Means in Odd Dimensions and EPD equations
Functional Analysis
2007-11-14 v1 Analysis of PDEs
Abstract
The paper contains a simple proof of the Finch-Patch-Rakesh inversion formula for the spherical mean Radon transform in odd dimensions. This transform arises in thermoacoustic tomography. Applications are given to the Cauchy problem for the Euler-Poisson-Darboux equation with initial data on the cylindrical surface. The argument relies on the idea of analytic continuation and known properties of Erdelyi-Kober fractional integrals.
Keywords
Cite
@article{arxiv.0711.1897,
title = {Spherical Means in Odd Dimensions and EPD equations},
author = {Boris Rubin},
journal= {arXiv preprint arXiv:0711.1897},
year = {2007}
}