Best polynomial approximation on the triangle

JOURNAL OF APPROXIMATION THEORY

卷:241

Article

Feng, Han¹  Krattenthaler, Christian²  Xu, Yuan³ 

[1] City Univ Hong Kong Kowloon, Dept Math, Hong Kong, Peoples R China

[2] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[3] Univ Oregon, Dept Math, Eugene, OR 97403 USA

关键词: Best polynomial approximation;    Orthogonal expansion;    Triangle;    K-functional;   

DOI  :  10.1016/j.jat.2019.01.005

来源: Elsevier

【 摘 要 】

Let E-n(f)(alpha,beta,gamma) denote the error of best approximation by polynomials of degree at most n in the space L-2 ((omega) over bar (alpha,beta,gamma)) on the triangle {(x, y) : x, y >= 0, x + y <= 1}, where (omega) over bar (alpha,beta,gamma) (x, y) := x(alpha) y(beta) (1 - x - y)(gamma )for alpha, beta, gamma > -1. Our main result gives a sharp estimate of E-n (f)(alpha,beta,gamma) in terms of the error of best approximation for higher order derivatives of f in appropriate Sobolev spaces. The result also leads to a characterization of E-n (f)(alpha,beta,gamma) by a weighted K-functional. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free