In the last two years the representation of harmonic functions defined only
through data on spheres with polar caps, has been studied by the authors,
using a set of functions orthonormal both on the sphere and on the data set
, which is a generalization of planar Slepian functions to the spherical ca
se. This idea can be applied for instance to derive the anomalous potential
T both at satellite's altitude and at ground level, from a set of satellit
e radial gradiometric observations, T-rr. The method has been compared with
a simple harmonic analysis showing a superior capability of retrieving the
unknown potential, particularly close to the polar caps. (C) 2000 Elsevier
Science Ltd. All rights reserved.