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

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Manuel Gräf

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  1. Manuel Gräf
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Correspondence to Manuel Gräf.

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Communicated by T. Sauer.

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Gräf, M. A unified approach to scattered data approximation on \(\mathbb{S}^{\bf 3}\) and SO(3). Adv Comput Math 37, 379–392 (2012). https://doi.org/10.1007/s10444-011-9214-3

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  • DOI: https://doi.org/10.1007/s10444-011-9214-3

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