English

An inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions

Analysis of PDEs 2012-08-29 v1

Abstract

In the articles [1] and [2] of D. Finch, M. Haltmeier, S. Patch and D. Rakesh inversion formulas were found in any dimension n2n\geq2 for recovering a smooth function with compact support in the unit ball from spherical means centered on the unit sphere. The aim of this article is to show that the methods used in [1], [2] can be modified in order to get similar inversion formulas from spherical means centered on an ellipsoid in two and three dimensional spaces.

Keywords

Cite

@article{arxiv.1208.5739,
  title  = {An inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions},
  author = {Yehonatan Salman},
  journal= {arXiv preprint arXiv:1208.5739},
  year   = {2012}
}

Comments

10 pages

R2 v1 2026-06-21T21:56:29.393Z