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Scattered data approximation on the rotation group and generalizations.

Aachen: Shaker, 2009, 130 S. (Zugl. München, Technische Universität, Fakultät für Mathematik, Diss., 2009) (Berichte aus der Mathematik)
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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 result in this regard is the establishment of Marcinkiewicz-Zygmund inequalities for scattered points on the rotation group. Finally, we shop how certain techniques and results can be generalized to study scattered data approcimation problems on locally compact groups.
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Publikationstyp Buch: Monographie
Typ der Hochschulschrift Dissertationsschrift
Schlagwörter Scattered Data Approximation; Marcinkiewicz-Zygmund Inequalities; Rotation Group; Positive Definite Functions; Wigner-D Functions; Stability; Random Polynomials
ISBN 978-3-8322-8288-2
Quellenangaben Band: , Heft: , Seiten: 130 S. Artikelnummer: , Supplement: ,
Reihe Berichte aus der Mathematik
Verlag Shaker
Verlagsort Aachen
Hochschule Technische Universität
Hochschulort München
Fakultät Fakultät für Mathematik