(untitled) (Analysis in Theory and Applications, 2017)
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(S^d-1 ) metric for 1q∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the L_q(S^d-1) metric for 1q∞.