Orlicz空间中二元多项式插值的逼近  

The Approximation of Bivariate Polynomial Interpolation in Orlicz Spaces

作　　者：李昕昕 吴嘎日迪[1,2] LI Xinxin;WU Garidi(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Center of Applied Mathematicse,Inner Mongolia Autonomous Region,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《应用数学》2024年第3期684-698,共15页Mathematica Applicata

基　　金：国家自然科学基金(11761055);内蒙古师范大学基本科研业务费专项资金资助(2023JBZD007)。

摘　　要：该文研究Orlicz空间中以Lissajous-Chebyshev结点为插值结点的二元多项式插值逼近问题.借助Holder不等式,光滑模等基本工具,利用Marcinkiewicz-Zygmund不等式及最佳单边逼近首先给出了Orlicz空间中高阶插值逼近的逼近度,其次研究了在不同情况下的二元插值逼近问题,利用光滑模,有界变差函数的总变差及最佳多项式逼近的阶给出了二元插值逼近度的估计.In this paper,we study the approximation problems of bivariate interpolation polynomial which takes Lissajous-Chebyshev nodes as the interpolation nodes in Orlicz spaces.Using tools such as Holder inequality,modulus of smoothness,Marcinkiewicz-Zygmund inequality and best one-side approximation,we first give the estimation of the degree of interpolation approximation in high dimensional Orlicz spaces.We also study the approximation problem of bivariate interpolation in different cases.By using modulus of smoothness,total variation of a bounded variation function and the degree of best polynomial approximation,we give the estimation of degree of approximation of bivariate interpolation.

关 键 词：插值多项式 Lissajous-Chebyshev结点 加权 光滑模 ORLICZ空间 

分 类 号：O174.41[理学—数学]