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Open Access Green as soon as Postprint is submitted to ZB.
Marcinkiewicz-Zygmund inequalities and polynomial approximation from scattered data on SO(3).
Numer. Funct. Anal. Optim. 29, 855-882 (2008)
We consider scattered data approximation problems on SO(3). To this end, we construct a new operator for polynomial approximation on the rotation group. This operator reproduces Wigner-D functions up to a given degree and has uniformly bounded Lp-operator norm for all 1 ? p ? ?. The operator provides a polynomial approximation with the same approximation degree of the best polynomial approximation. Moreover, the operator together with a Markov type inequality for Wigner-D functions enables us to derive scattered data Lp-Marcinkiewicz-Zygmund inequalities for these functions for all 1 ? p ? ?. As a major application of such inequalities, we consider the stability of the weighted least squares approximation problem on SO(3).
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Marcinkiewicz-Zygmund inequalities; Rotation group; Scattered data approximation; Wigner-D functions
ISSN (print) / ISBN
0163-0563
e-ISSN
1532-2467
Quellenangaben
Volume: 29,
Issue: 7-8,
Pages: 855-882
Publisher
Taylor & Francis
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)