This article primarily examines the approximation properties of a weighted Sobolev space W2,κr defined on a sphere Sd−1 equipped with Gaussian measures. Specifically, this study focuses on both the average… Click to show full abstract
This article primarily examines the approximation properties of a weighted Sobolev space W2,κr defined on a sphere Sd−1 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 W2,κr on Sd−1 are derived for these settings, providing a comprehensive understanding of their approximation characteristics.
Keywords:
spaces sphere;
approximation characteristics;
weighted sobolev;
sobolev spaces;
characteristics weighted;
approximation
Journal Title: Axioms
Year Published: 2025
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Journal Title: Axioms
Year Published: 2025
Link to full text (if available)
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recommendations!