Convergence rate for weighted polynomial approximation on the real line

JOURNAL OF APPROXIMATION THEORY

卷:272

Article

Kononova, Anna¹ 

[1] St Petersburg State Univ, Dept Math & Mech, Univ Sky Pr 28, St Petersburg 198504, Russia

关键词: Polynomial approximation;    Weighted spaces;    Rate of convergence;   

DOI  :  10.1016/j.jat.2021.105642

来源: Elsevier

【 摘 要 】

In this note we study a quantitative version of Bernstein's approximation problem when the polynomials are dense in weighted spaces on the real line completing a result of Mergelyan (1960). We estimate in the logarithmic scale the error of the weighted polynomial approximation of the Cauchy kernel. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free