English

Convergence of Julia polynomials

Complex Variables 2013-07-24 v1

Abstract

We study the approximation of conformal mappings with the polynomials defined by Keldysh and Lavrentiev from an extremal problem considered by Julia. These polynomials converge uniformly on the closure of any Smirnov domain to the conformal mapping of this domain onto a disk. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed through the smallest exterior angles at the boundary.

Keywords

Cite

@article{arxiv.1307.5835,
  title  = {Convergence of Julia polynomials},
  author = {Igor E. Pritsker},
  journal= {arXiv preprint arXiv:1307.5835},
  year   = {2013}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1307.5363

R2 v1 2026-06-22T00:55:43.899Z