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Keywords = Sobolev space with common smoothness

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22 pages, 352 KB  
Article
N-Widths of Multivariate Sobolev Spaces with Common Smoothness in Probabilistic and Average Settings in the Sq Norm
by Yuqi Liu, Xuehua Li and Huan Li
Axioms 2023, 12(7), 698; https://doi.org/10.3390/axioms12070698 - 17 Jul 2023
Cited by 4 | Viewed by 1845
Abstract
In this article, we give the sharp bounds of probabilistic Kolmogorov N,δ-widths and probabilistic linear N,δ-widths of the multivariate Sobolev space W2A with common smoothness on a Sq norm equipped with the Gaussian measure [...] Read more.
In this article, we give the sharp bounds of probabilistic Kolmogorov N,δ-widths and probabilistic linear N,δ-widths of the multivariate Sobolev space W2A with common smoothness on a Sq norm equipped with the Gaussian measure μ, where ARd is a finite set. And we obtain the sharp bounds of average width from the results of the probabilistic widths. These results develop the theory of approximation of functions and play important roles in the research of related approximation algorithms for Sobolev spaces. Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications)
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