一类多元Gauss-Weierstrass算子线性组合的加权Lp-逼近  

WEIGHTED Lp-APPROXIMATION BY A CLASS OF COMBINATIONS OF MULTIDIMENSIONAL GAUSS-WEIERSTRASS OPERATORS

作　　者：赵德钧[1] 

机构地区：[1]绍兴文理学院数学系

出　　处：《数学杂志》2006年第3期335-342,共8页Journal of Mathematics

基　　金：浙江省自然科学基金资助课题(102002)

摘　　要：本文研究一类多元Gauss-Weierstrass算子的线性组合加Jacobi型权逼近的性质,利用加权矩量不等式及加权K-泛函、光滑模等工具,建立了这类算子在Lp(1≤p≤∞)空间的正、逆定理和逼近阶的特征刻划.In this paper, we investigate the approximation characters of the weighted approximation with the Jacobi type weighted by a class of combinations of Gauss-Weierstrass operators, and by means of the inequalities of the weighted moments and the tools of functional, moduli of smoothness, we establish the direct and converse theorems and the characterization of approximation rate with these operators in the spaces.

关 键 词：多元Gauss-Weierstrass算子 多元线性组合 加权Lp-逼近 

分 类 号：O174.41[理学—数学]