L^p[-1,1](1p<∞)空间中复系数多项式的倒数逼近  

Approximation by Reciprocals of Polynomials with Complex Coefficients in L^p Spaces for 1p<∞

作　　者：梅雪峰[1] 

机构地区：[1]浙江教育学院数学系,杭州310012

出　　处：《工程数学学报》2003年第1期111-114,共4页Chinese Journal of Engineering Mathematics

基　　金：浙江省教育厅科研项目(20020145).

摘　　要：讨论了Lp[-1,1](1 p<∞)空间函数的复系数多项式的倒数逼近问题,证明了如下结论:设f(x)∈Lp[-1,1](1 p<∞),则存在一个次数不超过3n的复系数多项式Q3n(x)及一个仅与p有关的常数Mp>0使得　　f(x)-1Q3n(x)Lp[-1,1] Mpωφ(f,1 n)The approximation by reciprocals of polynomials with complex coefficients was discussed in Lp spaces for 1p<∞, obtain following result: if f(x)∈Lp(1p<∞),then there exists a 3n order polynomial with complex coefficients and a constant Mp>0 depending only on p such thatf(x)-1Q3n(x)LpMpωφ(f,1/n)L2p

关 键 词：多项式倒数逼近 DITZIAN-TOTIK模 JACKSON型估计 复系数多项式 

分 类 号：O174.42[理学—数学]