二元Gauss-Weierstrass算子线性组合的一致逼近  

Uniform Approximation of Linear Combinations of Binary Gauss-Weierstrass Operators

作　　者：钟宇 罗泽龙 官心果 曹德贤 ZHONG Yu;LUO Zelong;Guan xinguo;CAO Dexian(College of Preparatory Education,Qiannan Normal University for Nationalities,Duyun GuiZhou 558000;School of Mathematics and Statistics,Qiannan Normal University for Nationalities,Duyun GuiZhou 558000;Key Laboratory of Industrial Automation and Machine Vision of Qiannan,Duyun GuiZhou 558000;Bi Jie No.6 High School,Bijie Guizhou 551700)

机构地区：[1]黔南民族师范学院预科教育学院,贵州都匀558000 [2]黔南民族师范学院数学与统计学院,贵州都匀558000 [3]黔南州工业自动化与机器视觉重点实验室,贵州都匀558000 [4]毕节六中,贵州毕节551700

出　　处：《兴义民族师范学院学报》2024年第5期115-118,共4页Journal of Minzu Normal University of Xingyi

基　　金：贵州省教育厅高等学校科学研究项目(青年项目)“Gauss-Weierstrass算子的逼近”(项目编号:黔教技〔2022〕386号)。

摘　　要：通过介绍二元Gauss-Weierstrass算子线性组合,并借助K-泛函、光滑模二者之间的关系,首先对二元Gauss-Weierstrass算子的基本性质进行了分析,其次证明了该算子的有界性,最后构建了二元Gauss-Weierstrass算子线性组合在一致逼近意义下的一致逼近性质,并给出了逼近误差的估计。By introducing the linear combination of binary Gauss-Weierstrass operators,and leveraging the relationship between the K-functions and the smooth moduli,the basic properties of the binary Gauss-Weierstrass operator were analyzed,followed by a proof of its boundedness,and a consistent approximation property in the sense of uniform convergence was constructed for the binary Gauss-Weierstrass operator linear combination in the end.And an estimate of the approximation error was given.

关 键 词：K-泛函 光滑模 二元Gauss-Weierstrass算子 

分 类 号：O174.41[理学—数学]