Jackson-type inequalities on high-dimensional spheres  

作　　者：Yeli Niu Feng Dai 

机构地区：[1]Department of Mathematics,Shanghai Normal University,Shanghai 200234,China [2]Department of Mathematical and Statistical Sciences,University of Alberta,Edmonton,AB T6G2G1,Canada

出　　处：《Science China Mathematics》2024年第11期2571-2586,共16页中国科学（数学英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12201412);supported by the Natural Sciences and Engineering Research Council of Canada。

摘　　要：We study Jackson's inequality on high-dimensional spheres with respect to the modulus of smoothness defined via the rotation group.We obtain a version of Jackson's inequality with a dimensionfree constant,extending Newman and Shapiro's well-known results in 1964 from the case of r=1 and p=∞to more general cases.Our results partially overcome the curse of dimensionality.We also establish similar results on the equivalence of the K-functional and modulus of smoothness.

关 键 词：modulus of smoothness K-FUNCTIONAL Jackson's inequality high-dimensional approximation 

分 类 号：O178[理学—数学]