A modulus of smoothness on the unit sphere

被引：37
作者：
Ditzian, Z [1 ]
机构：
[1] Univ Alberta, Dept Math Sci, Edmonton, AB T6G 2G1, Canada
来源：
JOURNAL D ANALYSE MATHEMATIQUE | 1999年 / 79卷 / 1期
关键词：
Banach Space; Unit Sphere; Spherical Harmonic; Triangle Inequality; Orthogonal Matrix;
D O I：
10.1007/BF02788240
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For functions on Sd-1 (the unit sphere in R-d) and, in particular, for f is an element of L-p(Sd-1), we define new simple moduli of smoothness. We relate different orders of these moduli, and we also relate these moduli to best approximation by spherical harmonics of order smaller than n. Our new moduli lead to sharper results than those now available for the known moduli on L-p(Sd-1).
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页码：189 / 200
页数：12
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