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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 $$0<p<\infty$$.

### Most cited references13

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### Gaussian Measures

(1998)
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### Localized Polynomial Frames on the Ball

(2008)
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• Record: found
• Abstract: not found
• Article: not found

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

(1993)
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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