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

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          Abstract

          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 \(\lambda_n^{(a)}(W_{2,\mu}^r,\mu,L_{q,\mu})_p\), and obtain their asymptotic orders for all \(1\le q\le \infty\) and \(0<p<\infty\).

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          Most cited references 13

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          Gaussian Measures

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            Localized Polynomial Frames on the Ball

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              Average n-Widths of the Wiener Space in the L∞-Norm

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                Author and article information

                Journal
                2016-03-15
                Article
                1603.04578

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                41A46, 41A63, 42A61, 46C99
                math.CA math.FA

                Functional analysis

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