Copositive approximation by rational functions with prescribed numerator degree  

作　　者：YU Dan-sheng ZHOU Song-ping 

机构地区：[1]Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China Department of Mathematics, Statistic and Computer Science, St. Francis Xaiver University, Antigonish, Nova Scotia, Canada B2G 2W5 [2]Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310028, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2009年第4期411-416,共6页高校应用数学学报（英文版）（B辑）

基　　金：supported by the National Natural Science Foundation of China (10901044);Research Project of Hangzhou Normal University (YS05203154)

摘　　要：The paper proves that, if f（x） ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in （-1, 1）,then there exists a real rational function r（x） ∈ Rn^（2μ-1）l which is eopositive with f（x）, such that the following Jackson type estimate ｜｜f-r｜｜p≤Cδl^2μωφ（f,1/n）p holds, where μ is a natural number ≥3/2＋1/p, and Cδ is a positive constant depending only on δ.The paper proves that, if f（x） ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in （-1, 1）,then there exists a real rational function r（x） ∈ Rn^（2μ-1）l which is eopositive with f（x）, such that the following Jackson type estimate ｜｜f-r｜｜p≤Cδl^2μωφ（f,1/n）p holds, where μ is a natural number ≥3/2＋1/p, and Cδ is a positive constant depending only on δ.

关 键 词：copositive approximation rational functions approximation rate 

分 类 号：O172.2[理学—数学] O174.13[理学—基础数学]