Probabilistic and average linear widths of weighted Sobolev spaces on the ball equipped with a Gaussian measure

摘要

Let L-q,L-mu, 1 <= q <= infinity, denote the weighted L-q space of functions on the Euclidean unit ball B-d with respect to the weight (1 - parallel to x parallel to(2)(2))(mu-1/2), mu >= 0 and let W-2,mu(r) be the weighted Sobolev space on B-d equipped with a Gaussian measure nu. We investigate the probabilistic linear (n, delta)-widths lambda(n,delta )(W-2,mu(r), nu, L-q,L-mu) and the p-average linear n-widths lambda((a))(n) (W-2,mu(r), nu, L-q,L-mu)(p), and obtain their asymptotic orders for all 1 <= q <= infinity and 0 < p < infinity. (C) 2019 Elsevier Inc. All rights reserved.