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<p>We establish the representation theorem for Besov class with Dunkl weight on the unit sphere and apply it to obtain the approximation results of the near-best approximation operator. We also obtain the asymptotic orders of the entropy numbers, Kolmogorov <i>n</i>-widths, linear <i>n</i>-widths, and Gelfand widths of this class. Our results for Besov space extend the former work from the unweighted sphere to weighted setting (Dunkl weight), which show some sense of consistency.</p>

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Representation and approximation of weighted Besov classes on the sphere

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • Kai Wang,
  • Yali Wang,
  • Yinying Zhou

摘要

We establish the representation theorem for Besov class with Dunkl weight on the unit sphere and apply it to obtain the approximation results of the near-best approximation operator. We also obtain the asymptotic orders of the entropy numbers, Kolmogorov n-widths, linear n-widths, and Gelfand widths of this class. Our results for Besov space extend the former work from the unweighted sphere to weighted setting (Dunkl weight), which show some sense of consistency.