论文信息 - Multivariate approximating averages

Multivariate approximating averages

Averages on the sphere about x in Rd and on the rim of the cap about x in Sd-1 and their iterates are shown to be smoother than f. Furthermore, their approximating properties satisfy a strong converse inequality of type A when dealing with multivariate approximation (d ≥ 2 in case of Rd and d ≥ 3 in case of Sd-1). These results are in contrast to the classical results on R or T for which the situation is completely different.

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