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

Abstract

Optimal asymptotic orders of the probabilistic linear -widths of of the weighted Sobolev space equipped with a Gaussian measure ν are established, where , , denotes the space on with respect to the measure , .

Approximation Characteristics of Gel’fand Type in Multivariate Sobolev Spaces with Mixed Derivative Equipped with Gaussian Measure

“…Probabilistic and average widths have attracted much attention in recent years. We refer to the literature [7][8][9] for a survey. The usual widths may be found in the books [1,10].…”

“…Dai and Wang studied the probabilistic and average linear n-widths of diagonal matrices [17]. Zhai and Hu estimated the sharp bound of the probabilistic and average linear widths of Sobolev spaces with Jacobi weight [9]. Vasil'eva studied the Kolmogorov widths of intersections and Sobolev weighted classes [18,19].…”