Tensor Spherical Harmonics and Tensor Spherical Splines
نویسندگان
چکیده
In this paper, we deal with the problem of spherical interpolation of discretely given data of tensorial type. To this end, spherical tensor elds are investigated and a decomposition formula is described. It is pointed out that the decomposition formula is of importance for the spectral analysis of the gra-vitational tensor in (spaceborne) gradiometry. Tensor spherical harmonics are introduced as eigenfunctions of a tensorial analogue to the Beltrami operator and discussed in detail. Based on these preliminaries, a spline interpolation process is described and error estimates are presented. Furthermore, some relations between the spline basis functions and the theory of radial basis functions are developed.
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