Recovery of Atomic Measures on the Unit Sphere. (19th May 2022) - Filbir, Frank; Schröder, Kristof; Veselovska, Anna
Abstract: We study 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 it was considered by Y. de Castro & F. Gamboa ( J. Math. Anal. Appl. 395(1):336–354, 2012) and E. Candés & C. Fernandez-Granda ( J. Fourier Anal. Appl. 19(6):1229–1254, 2013). We construct a dual certificate using a kernel given in an explicit form and make a concrete analysis of the interpolation problem. Numerical examples are provided and analyzed.