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