On the Fourier transform of a class of generalized homogeneous functions

We consider a class of homogeneous functions of three variables with homogeneity degree $-1$ that are smooth on the unit sphere. We obtain relations that enable us to express the Fourier transform of such functions in terms of their values on the unit sphere. The Fourier transform is understood in the sense of generalized functions. We show that the relations obtained can be used to construct three-dimensional cone-beam tomographic reconstruction algorithms.