Generalized translation operator and approximation in several variables

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:178

Article; Proceedings Paper

Xu, Y

关键词: translation operator;    modulus of smoothness;    K-functional;    best approximation;    several variables;   

DOI  :  10.1016/j.cam.2004.02.029

来源: Elsevier

【 摘 要 】

Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to define convolution structures and modulus of smoothness for these regions, which are in turn used to characterize the best approximation by polynomials in the weighted LP spaces. In one variable, this becomes the generalized translation operator for the Gegenbauer polynomial expansions. (c) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free