修正的Gauss-Weierstrass积分算子在Orlicz空间内的指数加权逼近  

Exponential Weighted Approximation of the Modi ed Gauss-Weierstrass Integral Operators in Orlicz Spaces

作　　者：陈琳 吴嘎日迪[1,2,3] CHEN Lin;WU Garidi(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Laboratory of In nite-dimensional Hamiltonian System and Its Algorithm Application,Ministrg of Education,Hohhot 010022,China;Center for Applied Mathematics of Inner Mongolia Autonomous Regin,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]无穷维哈密顿系统及其算法应用教育部重点实验室,内蒙古呼和浩特010022 [3]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4期1114-1120,共7页Mathematica Applicata

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

摘　　要：本文研究修正的Gauss-Weierstrass积分算子在指数加权Orlicz空间内的逼近问题.通过在指数加权Orlicz空间内建立逼近问题的相关引理,并结合Orlicz空间内的光滑模,Korovkin定理及相关分析技巧得出了该算子在指数加权Orlicz空间内的逼近正定理以及相关逼近性质.This article studied the approximation problem of a modi ed Gauss-Weierstrass integral operators in an exponentially weighted Orlicz spaces.By establishing relevant lemmas for approximation problems in an exponentially weighted Orlicz spaces,and combining smooth module,the Korovkin theorem,and related analysis techniques,the positive approximation theorem and related approximation properties of operators in an exponentially weighted Orlicz spaces are obtained.

关 键 词：Gauss-Weierstrass积分算子 ORLICZ空间 逼近 

分 类 号：O174.41[理学—数学]