RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP -In memory of Professor Sun Yongsheng  

作　　者：Kunyang Wang Feng Dai 

机构地区：[1]School of Mathematical Sciences Beijing Normal University Beijing, 100875 P. R. China [2]Department of Mathematical and Statistical Sciences CAB 632 University of Alberta Edmonton, Alberta Canada T6 2G1

出　　处：《Analysis in Theory and Applications》2007年第1期50-63,共14页分析理论与应用（英文刊）

基　　金：Supported by the NSF of China under the Grant 10471010;partially by the NSERC Canada under Grant G121211001

摘　　要：As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.

关 键 词：spherical harmonics Fourier-Laplace expansion convergence APPROXIMATION SMOOTHNESS K-FUNCTIONAL width 

分 类 号：O241.8[理学—计算数学]