Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting
Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 2 : pp. 154–166
Abstract
In this paper, we study optimal recovery (reconstruction) of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the $L_q({\mathbb{S}^{d-1}})$ metric for $1\le q\le \infty$, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the $L_q(\mathbb{S}^{d-1})$ metric for $1\le q\le \infty$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n2.5
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 2 : pp. 154–166
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Optimal recovery on the sphere average sampling numbers optimal algorithm Gaussian measure.