A unified approach to scattered data approximation on $\mathbb{S}^{\bf 3}$ and SO(3)

Authors:
Manuel Gräf
Affiliations:
Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany 09107
Venue:
Advances in Computational Mathematics
Year:
2012

Citing 3
Cited 0

Corrigendum to "Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature"

Mathematics of Computation
Radial Basis Functions

Radial Basis Functions
A survey on spherical designs and algebraic combinatorics on spheres

European Journal of Combinatorics

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Abstract

In this paper we use the connection between the rotation group SO(3) and the three-dimensional Euclidean sphere $\mathbb{S}^{3}$ in order to carry over results on the sphere $\mathbb{S}^{3}$ directly to the rotation group SO(3) and vice versa. More precisely, these results connect properties of sampling sets and quadrature formulae on SO(3) and $\mathbb{S}^{3}$ 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 sphere $\mathbb{S}^{3}$ , respectively.