We consider approximation methods defined by translates of a positive definite function on a compact group. A characterization of the native space generated by a positive definite function on a compact group is presented. Starting from Bochner's theorem, we construct examples of well-localized positive definite central functions on the rotation group [image omitted](3). Finally, the stability of the interpolation problem and the error analysis for the given examples are studied in detail.
Approximation by positive definite functions on compact groups
Erb W.;
2008
Abstract
We consider approximation methods defined by translates of a positive definite function on a compact group. A characterization of the native space generated by a positive definite function on a compact group is presented. Starting from Bochner's theorem, we construct examples of well-localized positive definite central functions on the rotation group [image omitted](3). Finally, the stability of the interpolation problem and the error analysis for the given examples are studied in detail.
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