THE SHARP JACKSON INEQUALITY FOR L^2-APPROXIMATION ON THE PERIODIC CYLINDER  

作　　者：谷懿 刘永平 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University

出　　处：《Acta Mathematica Scientia》2015年第2期375-382,共8页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(11071019);Beijing Natural Science Foundation(1132001)

摘　　要：We consider Jackson inequality in L^2 （B^d×T, Wκ,μ^B （x））, where the weight function Wκ,μ^B （X） is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-1（f）2≤κn,m（τ,r）ωr（f,t）2,τ≥2τn,λ,where Tn,λ is the first positive zero of the Gegenbauer cosine polynomial Cn^λ （cos θ）（n ∈ N）.We consider Jackson inequality in L^2 （B^d×T, Wκ,μ^B （x））, where the weight function Wκ,μ^B （X） is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-1（f）2≤κn,m（τ,r）ωr（f,t）2,τ≥2τn,λ,where Tn,λ is the first positive zero of the Gegenbauer cosine polynomial Cn^λ （cos θ）（n ∈ N）.

关 键 词：Jackson inequality best approximation modulus of continuity weight function 

分 类 号：O178[理学—数学] TP311.11[理学—基础数学]