Approximation Characteristics of Weighted Sobolev Spaces on Sphere in Different Settings - Jiayi Qiu; Guanggui Chen; Yanyan Xu; Ying Luo; Hang Ren (Axioms)
This article primarily examines the approximation properties of a weighted Sobolev space <semantics><msubsup>W2,κr</msubsup></semantics> defined on a sphere <semantics>Sd−1</semantics> equipped with Gaussian measures. Specifically, this study focuses on both the average case and probabilistic case settings. The exact asymptotic orders of the Gel’fand n-width and the linear n-width of <semantics><msubsup>W2,κr</msubsup></semantics> on <semantics>Sd−1</semantics> are derived for these settings, providing a comprehensive understanding of their approximation characteristics.