Some analytic properties of the cone transform

This paper addresses the cone transform that integrates a function over the surfaces of circular cones. We derive an inversion formula for the cone transform in n -dimensional Euclidean space for cones having a fixed central axis direction, but having all opening angles and vertices. We also show that the cone transform and its dual are Fourier integral operators, and the normal operator is a pseudo-differential operator. We finally present a differential equation that the cone transform satisfies, which can be seen as a first step in describing the range of the cone transform.