Minimax principle and lower bounds in H2-rational approximation

JOURNAL OF APPROXIMATION THEORY

卷:206

Article

Baratchart, Laurent¹  Chevillard, Sylvain¹  Qian, Tao² 

[1] Inria, 2004 Route Lucioles,BP 93, F-06902 Sophia Antipolis, France

[2] Univ Macau, Fac Sci & Technol, E11 Ave Univ, Taipa, Macao, Peoples R China

关键词: Complex rational approximation;    Hardy spaces;    Lower bounds;    Error rates;   

DOI  :  10.1016/j.jat.2015.03.004

来源: Elsevier

【 摘 要 】

We derive lower bounds in rational approximation of given degree to functions in the Hardy space H-2 of the unit disk. We apply these to asymptotic error rates in rational approximation to Blaschke products and to Cauchy integrals on geodesic arcs. We also explain how to compute such bounds, either using Adamjan-Arov-Krein theory or linearized errors, and we present a couple of numerical experiments. We dwell on a maximin principle developed in Baratchart and Seyfert (2002). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free