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

Abstract: In the articles [1] and [2] of D. Finch, M. Haltmeier, S. Patch and D. Rakesh inversion formulas were found in any dimension $n\geq2$ 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.