Scattered data approximation problems on the rotation group naturally arise in diverse fields in science and engineering. In this thesis, we establish the theoretical foundations of various approaches to such problems. Firstly, we consider interpolation procedures defined by positive definite basis functions on the rotation group and study this process in great detail. Subsequently, we address ourselves to polynomial approximation methods for scattered data on the rotation group. A central result in this regard is the establishment of Marcinkiewicz-Zygmund inequalities for scattered points on the rotation group.
Finally, we show how certain techniques and results can be generalized to study scattered data approximation problems on locally compact groups.
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Scattered data approximation problems on the rotation group naturally arise in diverse fields in science and engineering. In this thesis, we establish the theoretical foundations of various approaches to such problems. Firstly, we consider interpolation procedures defined by positive definite basis functions on the rotation group and study this process in great detail. Subsequently, we address ourselves to polynomial approximation methods for scattered data on the rotation group. A central resul...
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