@Article{ATA-31-154,
author = {Z. X. Huang and H. P. Wang},
title = {Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting},
journal = {Analysis in Theory and Applications},
year = {2017},
volume = {31},
number = {2},
pages = {154--166},
abstract = {<p style="text-align: justify;">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 $1\le q\le \infty$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2015.v31.n2.5},
url = {http://global-sci.org/intro/article_detail/ata/4630.html}
}