In this talk, we discuss the problem of recovering an atomic measure on the unit 2-sphere S^2 given finitely many moments with respect to spherical harmonics. The analysis relies on the formulation of this problem as an optimization problem on the space of bounded Borel measures on S^2 as suggested by Y. de
Castro & F. Gamboa and E. Candes & C. Fernandez-Granda. We construct a dual certificate using a kernel given in an explicit form and make a concrete analysis of the interpolation problem. We support our theoretical results by various numerical examples related to direct solution of the optimization
problem and its discretization.
This is a joint work with Frank Filbir and Kristof Schroder.