English

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}
}
R2 v1 2026-06-21T09:42:46.035Z