{"paper":{"title":"Probabilistic and average linear widths of weighted Sobolev spaces on the ball equipped with a Gaussian measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Heping Wang","submitted_at":"2016-03-15T07:30:32Z","abstract_excerpt":"Let $L_{q,\\mu}$, $1\\leq q\\leq\\infty$, denotes the weighted $L_q$ space of functions on the unit ball $\\Bbb B^d$ with respect to weight $(1-\\|x\\|_2^2)^{\\mu-\\frac12},\\,\\mu\\ge 0$, and let $W_{2,\\mu}^r$ be the weighted Sobolev space on $\\Bbb B^d$ with a Gaussian measure $\\nu$. We investigate the probabilistic linear $(n,\\delta)$-widths $\\lambda_{n,\\delta}(W_{2,\\mu}^r,\\nu,L_{q,\\mu})$ and the $p$-average linear $n$-widths\n $\\lambda_n^{(a)}(W_{2,\\mu}^r,\\mu,L_{q,\\mu})_p$, and obtain their asymptotic orders for all $1\\le q\\le \\infty$ and $0