Range conditions for a spherical mean transform
Analysis of PDEs
2011-10-04 v3 Mathematical Physics
math.MP
Abstract
The paper is devoted to the range description of the Radon type transform that averages a function over all spheres centered on a given sphere. Such transforms arise naturally in thermoacoustic tomography, a novel method of medical imaging. Range descriptions have recently been obtained for such transforms, and consisted of smoothness and support conditions, moment conditions, and some additional orthogonality conditions of spectral nature. It has been noticed that in odd dimensions, surprisingly, the moment conditions are superfluous and can be eliminated. It is shown in this text that in fact the same happens in any dimension.
Keywords
Cite
@article{arxiv.0902.4272,
title = {Range conditions for a spherical mean transform},
author = {Mark Agranovsky and David Finch and Peter Kuchment},
journal= {arXiv preprint arXiv:0902.4272},
year = {2011}
}