紧李群上的多项式逼近(Ⅱ)——按L_p模的最佳逼近  

Approximation by Polynomials on Compact Lie Groups in the Lp Norm(Ⅱ)

作　　者：郑学安[1] 赵和生[1] 许增福[1] 

机构地区：[1]安徽大学

出　　处：《数学进展》1990年第2期199-203,共5页Advances in Mathematics（China）

摘　　要：设G为一紧李群，A_R表示G上全体R阶三角多项式，即用表示且具有直到阶的任意按模的偏导数此处,均为非负整数是G的李代数关于拟Cartan内积的么正基.而用(G)表示且对时的连续模不超过.In this paper the Jackson's and Bernstein's theorems of the hest approximation by trigonometric polynomials on compact Lie groups in the Lp norm are proved.In order to prove the theorems, we studied the generralized Riesz means of order 5 and degree a on compact Lie groups defined hy function (1 -ta)+ for a,>0 and obtained a series of results about generalized Riesz means.

关 键 词：紧李群 多项式逼近 Lp模 最佳逼近 

分 类 号：O177.5[理学—数学]