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.   In this paper we consider a certain class of geodetic linear inverse problems  in a reproducing kernel Hilbert space setting to obtain a bounded inverse operator . For a numerical realization we assume  to be given at a finite number of discrete points to which we employ a spherical spline interpolation method adapted to the Hilbert spaces. By applying  to the obtained spline interpolant we get an approximation of the solution . Finally our main task is to show some properties of the approximated solution and to prove convergence results if the data set increases.

The solution of linear inverse problems in satellite geodesy by means of spherical spline approximation