On weighted approximation with Jacobi weights

JOURNAL OF APPROXIMATION THEORY

卷:237

Article

Kopotun, K. A.¹  Leviatan, D.²  Shevchuk, I. A.³ 

[1] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

[2] Tel Aviv Univ, Raymond & Beverly Sackler Sch Math Sci, IL-6139001 Tel Aviv, Israel

[3] Natl Taras Shevchenko Univ Kyiv, Fac Mech & Math, UA-01033 Kiev, Ukraine

关键词: Approximation by polynomials in weighted L-p-norms;    Degree of approximation;    Direct and inverse theorems;    Jacobi weights;    Moduli of smoothness;    Characterization of smoothness classes;    Whitney-type estimates;   

DOI  :  10.1016/j.jat.2018.09.003

来源: Elsevier

【 摘 要 】

We obtain matching direct and inverse theorems for the degree of weighted L p -approximation by polynomials with the Jacobi weights (1 - x)(alpha) (1 + x)(beta) . Combined, the estimates yield a constructive characterization of various smoothness classes of functions via the degree of their approximation by algebraic polynomials. In addition, we prove Whitney type inequalities which are of independent interest. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free