A Geometric Approach to Polynomial and Rational Approximation
Complex Variables
2023-02-14 v2 Dynamical Systems
Abstract
We strengthen the classical approximation theorems of Weierstrass, Runge and Mergelyan by showing the polynomial and rational approximants can be taken to have a simple geometric structure. In particular, when approximating a function on a compact set , the critical points of our approximants may be taken to lie in any given domain containing , and all the critical values in any given neighborhood of the polynomially convex hull of .
Cite
@article{arxiv.2301.02888,
title = {A Geometric Approach to Polynomial and Rational Approximation},
author = {Christopher J. Bishop and Kirill Lazebnik},
journal= {arXiv preprint arXiv:2301.02888},
year = {2023}
}