Uniform polynomial approximation with A* weights having finitely many zeros

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Kopotun, Kirill A.¹ 

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

关键词: Doubling weights;    A* weights;    Weighted moduli of smoothness;    Polynomial approximation;    Direct and inverse theorems;    Realization functionals;   

DOI  :  10.1016/j.jmaa.2015.10.063

来源: Elsevier

【 摘 要 】

We prove matching direct and inverse theorems for uniform polynomial approximation with A* weights (a subclass of doubling weights suitable for approximation in the L-infinity norm) having finitely many zeros and not too rapidly changing away from these zeros. This class of weights is rather wide and, in particular, includes the classical Jacobi weights, generalized Jacobi weights and generalized Ditzian-Totik weights. Main part and complete weighted moduli of smoothness are introduced, their properties are investigated, and equivalence type results involving related realization functionals are discussed. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free