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