Reconstruction from local discrete averages on the plane

The aim of the paper is to construct a solution for the equation f ⋆ μ = g , where f ⋆ μ is the convolution of f and μ given by ∫ R 2 f ( x ¯ − y ¯ ) d μ ( y ¯ ) , g is an arbitrary continuous function and μ is a finitely supported measure on the plane.