On Lagrange polynomials and the rate of approximation of planar sets by polynomial Julia sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Bialas-Ciez, Leokadia¹  Kosek, Marta¹  Stawiska, Malgorzata² 

[1] Jagiellonian Univ, Fac Math & Comp Sci, Inst Math, Lojasiewicza 6, PL-30348 Krakow, Poland

[2] Math Reviews, 416 Fourth St, Ann Arbor, MI USA

关键词: Lagrange polynomials;    Lebesgue constants;    Green function;    Julia sets;   

DOI  :  10.1016/j.jmaa.2018.04.029

来源: Elsevier

【 摘 要 】

We revisit the approximation of nonempty compact planar sets by filled-in Julia sets of polynomials developed in [27] and analyze the rate of approximation. We use slightly modified fundamental Lagrange interpolation polynomials and show that taking certain classes of nodes with subexponential growth of Lebesgue constants improves the approximation rate. To this end we investigate properties of some arrays of points in C. In particular we prove subexponential growth of Lebesgue constants for pseudo Leja sequences with bounded Edrei growth on finite unions of quasiconformal arcs. Finally, for some classes of sets we estimate more precisely the rate of approximation by filled-in Julia sets in Hausdorff and Klimek metrics. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free