TY - JOUR
T1 - Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting
JO - Analysis in Theory and Applications
VL - 2
SP - 154
EP - 166
PY - 2017
DA - 2017/04
SN - 31
DO - http://doi.org/10.4208/ata.2015.v31.n2.5
UR - https://global-sci.org/intro/article_detail/ata/4630.html
KW - Optimal recovery on the sphere, average sampling numbers, optimal algorithm, Gaussian measure.
AB - <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>