The Slepian Problem on the Sphere

The Slepian problem consists in determining a sequence of functions that constitute an orthonormal basis of a subset of ℝ, (or ℝ2) concentrating the maximum information in the subspace of square integrable function with bandfinite spectrum. The same problem can be stated and solved on the sphere.The relation between the new basis and the ordinary spherical harmonic basis can beexplicitely written and numerically studied.What turns out is that this tool is a natural solution to capture the maximum amount of information from a non-polar gradiometric mission.