Weighted approximation for weak convex external fields

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Benko, David

关键词: Weighted approximation;    Polynomials;    Equilibrium measure;    Logarithmic potential;   

DOI  :  10.1016/j.jmaa.2011.06.060

来源: Elsevier

【 摘 要 】

Let w(x) not equivalent to 0 be a non-negative continuous weight function which decays faster than 1/x near infinity and let q(x) = -log w(x). Totik proved that if q(x) is convex, then a continuous function f(x) can be approximated by weighted polynomials w(x)P-n(n)(x), n = 0, 1,2, ..., if and only if f(x) vanishes outside the support of the equilibrium measure associated with q(x). We prove a similar result in the case when q(x) is only weak convex. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free