On the Degree of Approximation by Spherical Translations  

作　　者：Bao-huai Sheng 

机构地区：[1]Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China

出　　处：《Acta Mathematicae Applicatae Sinica》2006年第4期671-680,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10471130,10371024);the Natural Science Fund of Zhejiang Province(No:Y604003)

摘　　要：The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^2（S^q） norms of the orthogonal projection operators of the translated function are zeros. In the present paper we show that the spherical translations share the same degree of approximation as that of spherical harmonics.The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^2（S^q） norms of the orthogonal projection operators of the translated function are zeros. In the present paper we show that the spherical translations share the same degree of approximation as that of spherical harmonics.

关 键 词：Spherical harmonics translation class degree of approximation 

分 类 号：O241.5[理学—计算数学]