OPTIMAL BIRKHOFF INTERPOLATION AND BIRKHOFF NUMBERS IN SOME FUNCTION SPACES  

作　　者：许贵桥 刘永平 郭丹丹 Guiqiao XU;Yongping LIU;Dandan GUO(Department of Mathematics,Tianjin Normal University,Tianjin,300387,China;Department of Mathematics,Beijing Normal University,Beijing,100875,China)

机构地区：[1]Department of Mathematics,Tianjin Normal University,Tianjin,300387,China [2]Department of Mathematics,Beijing Normal University,Beijing,100875,China

出　　处：《Acta Mathematica Scientia》2023年第1期125-142,共18页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(11871006,11671271)。

摘　　要：This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

关 键 词：optimal Birkhoff interpolation Birkhoff number Sobolev space worst case setting 

分 类 号：O177[理学—数学]