Entropy numbers of weighted Sobolev classes on the unit sphere

TL;DR

This paper determines the asymptotic behavior of entropy numbers for weighted Sobolev classes on the unit sphere, ball, and simplex, incorporating Dunkl weights related to reflection groups.

Contribution

It provides the first asymptotic order results for entropy numbers of weighted Sobolev classes with Dunkl weights on these geometric domains.

Findings

Asymptotic orders of entropy numbers on the unit sphere with Dunkl weights

Extension of results to the unit ball and standard simplex

Insights into the approximation properties of weighted Sobolev classes

Abstract

We obtain the asymptotic orders of entropy numbers of Sobolev classes on the unit sphere with Dunkl weight which associates with the finite reflection group. Moreover, the asymptotic order of entropy numbers of weighted Sobolev classes on the unit ball and on the standard simplex are discussed.