L_[0,1]~p(1

A Generalization on Approximation by Reciprocals of Polynomials With Positive Coefficients in L_[0,1]~p Spaces for 1 我的收藏 名 称： 注 释：

作　　者：梅雪峰[1] 周颂平[2] 

机构地区：[1]浙江教育学院数学系,杭州浙江310012 [2]浙江工程学院理学院,杭州浙江310018

出　　处：《数学进展》2005年第6期707-716,共10页Advances in Mathematics（China）

基　　金：The Research Project of the Education Department of Zhejiang Province,supported in party by National and Zhejiang Provincial Natural Science Foundations of China(No.10141001,No.101009).

摘　　要：本文推广了L[0,1]p(1<p<∞)空间函数的正系数多项式的倒数逼近的结论,即证明了:设f(x)∈L[0,1]p,(1<p<∞),且在(0,1)内严格1次变号,则存在一点x0∈(0,1)及一个n次多项式Rn(x)∈∏n(+)使得其中∏n(+)为次数不超过n的正系数多项式的全体．The present paper gives a generalization of approximation by reciprocals of polynomials with positive coefficients in L[0,1]^p Spaces for 1〈0〈∞ and proves that if f（x）∈L[0,1]^p,1〈p〈∞, changes its sign once in the interval （0, 1）, then there exists an xo E （0, 1） and a polynomial Pn（x）∈Πn（＋） such that ‖f（x）-x-x0/Pn（x）‖L[0,1]^p≤Cpω（f,n^-1/2）L[0,1]^p,where Πn（＋） indicates all polynomials of degree n with positive cocfficients.

关 键 词：多项式倒数逼近 Steklov函数 修正的Jackson核 

分 类 号：O174.42[理学—数学]