Diagonal spherical means
We introduce a mean for functions and distributions of two vector variables, (Formula presented.) , the diagonal spherical mean K, defined as (Formula presented.) We study several properties of these means as well as identities satisfied by them. We show that the Dirac delta function in the diagonal of the unit ball (Formula presented.) in (Formula presented.) admits a representation as the diagonal spherical mean of certain kernels κ, (Formula presented.) distributionally for (Formula presented.). These representations of the delta function solve the problem of reconstruction of a distribution with compact support inside (Formula presented.) if its standard spherical Radon transform is known in the boundary (Formula presented.).
Publication Source (Journal or Book title)
Integral Transforms and Special Functions
Estrada, R. (2015). Diagonal spherical means. Integral Transforms and Special Functions, 26 (10), 796-811. https://doi.org/10.1080/10652469.2015.1052428