Probabilistic linear widths of Sobolev space with Jacobi weights on [ − 1 , 1 ] $[-1,1]$

Journal of Inequalities and Applications

Xiuyan Hu¹  Xuebo Zhai¹ 

[1] School of Mathematical and Statistics, Zaozhuang University;

关键词: probabilistic linear widths;    Jacobi weights;    weighted Sobolev classes;    Gaussian measure;   

DOI  :  10.1186/s13660-017-1540-7

来源: DOAJ

【 摘 要 】

Abstract Optimal asymptotic orders of the probabilistic linear ( n , δ ) $(n,\delta)$ -widths of λ n , δ ( W 2 , α , β r , ν , L q , α , β ) $\lambda_{n,\delta }(W^{r}_{2,\alpha,\beta }, \nu,L_{q,\alpha,\beta })$ of the weighted Sobolev space W 2 , α , β r $W_{2,{\alpha, \beta }}^{r}$ equipped with a Gaussian measure ν are established, where L q , α , β $L_{q,\alpha,\beta }$ , 1 ≤ q ≤ ∞ $1\leq q\leq \infty $ , denotes the L q $L_{q}$ space on [ − 1 , 1 ] $[-1,1]$ with respect to the measure ( 1 − x ) α ( 1 + x ) β $(1-x)^{\alpha }(1+x)^{\beta }$ , α , β > − 1 / 2 $\alpha,\beta > -1/2$ .

【 授权许可】

Unknown