N-Widths of Multivariate Sobolev Spaces with Common Smoothness in Probabilistic and Average Settings in the Sq Norm

doi:10.3390/axioms12070698

Yuqi Liu, Xuehua Li, Huan Li

N-Widths of Multivariate Sobolev Spaces with Common Smoothness in Probabilistic and Average Settings in the Sq Norm

Geometry and Topology
Logic
Mathematical Physics
Algebra and Number Theory
Analysis

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 A⊂Rd 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.

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N-Widths of Multivariate Sobolev Spaces with Common Smoothness in Probabilistic and Average Settings in the Sq Norm

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