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Manuel Gräf : An unified approach to scattered data approximation on S3 and SO(3)

Manuel Gräf : An unified approach to scattered data approximation on S3 and SO(3)

Author(s):
Manuel Gräf
Title:
An unified approach to scattered data approximation on S3 and SO(3)
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 2, 2010
Mathematics Subject Classification:
65T99 [ ]
43A90 [ ]
65D32 [ ]
Abstract:
In this paper we use the connection between the rotation group SO(3) and the three-dimensional Euclidean sphere S3 in order to carry over results of the three-sphere directly to the rotation group and vice versa. More precisely, these results connect properties of sampling sets and quadrature formulae on SO(3) and S3, respectively. Furthermore we relate Marcinkiewicz-Zygmund inequalities and conditions for the existence of positive quadrature formulae on the rotation group SO(3) to those on the three-sphere S3, respectively.
Keywords:
rotation group SO(3), three-sphere S3, quaternions, scattered data, sampling sets, quadrature formulae, Marcinkiewicz-Zygmund inequalities
Language:
English
Publication time:
03/2010