Remarks on the general Funk-Radon transform and thermoacoustic tomography
arXiv:math/0701204
Abstract
We study properties of the general integral transform defined for a family of hypersurfaces in a smooth manifold. Estimates of Sobolev norms, range conditions and approximation theorem for the kernel of the integral transform are stated. Applications to the spherical mean transform that appears in thermo/opto/photoacoustic tomography are discussed.